[Music] candidates are expected to have a thorough understanding of the syllabus details outlined in the accompanying figure physical quantities there are two types of physical quantities as scalar and Vector all physical quantities consist of a numerical magnitude and a unit for example the volume of 150 cubic M the volume is the physical quantity it is a scalar quantity because the volume has know the direction the value of 150 represents the numerical magnitude or size of the volume the cubic meters represents the unit of volume the weight of 500 Newtons the weight is physical quantity it is a vector quantity because it has both magnitude and Direction the value of 500 represents the numerical magnitude or size of the weight the Newton is the unit of weight the direction of weight is always downward scalar and Vector a scalar quantity has only magnitude or size which is a numerical value a vector quantity has both magnitude and direction for example some scalar quantities in physics include distance speed time mass volume energy and density for example some Vector quantities in physics include displacement velocity acceleration weight Force momentum and gravitational field strength this and displacement you don't need to know about displacement for IGCSE but it useful to know it when a ball travels along a circular track from point A to point B the distance traveled from A to B is half of the circumference of the circle the displacement is the diameter of a circle and its direction point from A to B or downward or South when a ball travels back to point a the distance traveled from point a to return at Point a is equal to the circumference of a circle the displacement is equal to zero this is because the ball has returned to its original position therefore we can deduce that distance is the total length of the path traveled by an object distance is a scalar quantity which means that it has only magnitude and no direction and its unit is meter the displacement is the directed distance from the start to the end points displacement is a vector quantity which means that it has both magnitude and Direction and its unit is meter speed and velocity average speed is the total distance moved per unit time speed is a scalar quantity which has only magnitude its unit is m/s velocity is a speed in a given Direction velocity is a vector quantity which has both magnitude and Direction the unit of velocity is the same as the unit of speed which is m/s the magnitude of velocity is equal to speed when an object travels in a straight line and does not change its direction a car traveling at an initial speed of U for T seconds reaches a final speed of v and covers a distance of s m and its acceleration is constant so the average speed is U + V / 2 total distance moved is s total time is T therefore U + V / 2 = s/ T you don't need to remember this equation If U equals V this means a car is traveling with constant speed so the average speed is V total distance moved is s total time is T therefore V = s/ T acceleration acceleration is change in velocity per unit time acceleration is a vector quantity which has both magnitude and Direction its unit is m/s squared therefore the equation of acceleration is a equal V - U / t a is acceleration in m/s squared V is final velocity in m/s U is initial velocity in m/s and T is time taken in seconds When U equals V it indicates the car is traveling at a constant speed the change in speed is zero the acceleration is also zero when V is more than U it indicates the car is speeding up this positive change in velocity is called a acceleration when V is less than U it indicates the car is slowing down this negative change in velocity is called deceleration if a car is moving with uniform acceleration a we will get the equation for u v a s as V ^2 = U ^2 + 2 a s if a car moves the same distance as 5 m every second this means that a car is TR traveling with constant speed of 5 m/s and acceleration is zero if a car moves with increasing distance every second this means that a car is traveling with increasing speed and it is accelerating if a car moves with decreasing distance every second this means that a car is traveling with decreasing speed and it is decelerating investigate the motion of a toy car this experiment explores the relationship between the height h of a wooden track and the average speed of a toy car traveling down it begin by setting up the apparatus as shown securely clamp the wooden track at the desired height H measure height with a meter rule ensuring the meter rule is perpendicular to the bench we use the set Square to check that a meter rule perpendicular to the bench measure the distance between points A and B using a meter rule measure the time it takes for the car to travel distance a using a stopwatch human reaction time can introduce errors when using a stopwatch to minimize this error repeat the time measurement at least three times for each height H and calculate the average time always release the car from the same starting point a record your results in a table similar to the one shown to find the average speed you will use the equation average speed equals distance moved AB divided by time taken distance time graph the graph of distance Against Time as shown here we draw a right triangle here is change in X and the X AIS represents time here is change in y and the y- AIS represents distance the gradient of graph is the ratio of the change in y AIS to change in x-axis so it is the ratio of the change in distance to change in time since the gradient of the graph is the speed of the object a horizontal line graph with zero gradient indicates the speed is zero and no acceleration so the object is at rest a straight line graph with constant gradient indicates the object object is moving at a constant speed and no acceleration a is steeper than b so a has a higher speed than b a curved graph with an increasing gradient indicates the object is moving at increasing speed and it is accelerating a curved graph with a decreasing gradient indicates the object is moving at decreasing speed and it is decelerating finding the speed and average speed using distance time graph the distance time graph is shown here between a to B shows that the gradient is increasing so the speed is also increasing and the object is accelerating between B to C shows that the gradient is constant so the speed is also constant and the acceleration is zero we can find the constant speed by the gradient between B to C we draw a right triangle here is changing X or run is equal to 20 - 7.5 is equal to 12.5 here is change in y or rise is equal to 45 - 10 is equal to 35 therefore the speed is equal to 35 / 12.5 is equal to 2.8 m/s between C to D shows that the gradient is decreasing so the speed is also decreasing and the object is decelerating between D to e shows that the gradient is zero so the speed is zero no acceleration and the object is at rest we can find the average speed between a to e by the total distance divided by total time taken the total distance is 60 M the total time is 35 seconds therefore the average speed is equal to 60 / by 35 is equal to 1.71 m/s velocity time graph the graph of velocity Against Time as shown here we draw a right triangle here is change in X and the x-axis represents time here is change in y and the y- AIS represents velocity the gradient of velocity time graph is the ratio of the change in y- AIS to the change in x-axis so it is the ratio of change in velocity to change in time since the gradient of the graph is the acceleration of the object the area under graph is the half of U + V * T this is the average velocity or speed since the area under graph is the distance moved the speed at any point is simply found by reading the value of the Velocity axis this is because velocity is speed in a given Direction their magnitude are equal when an object travels in a straight line and does not change its direction a horizontal line graph at the x-axis with zero gradient indicates the acceleration is zero and a speed is zero so the object is at rest a horizontal line graph with zero gradient indicates the acceleration is zero and the object is moving at constant speed of U since the distance moved is the area under graph which is U * t a straight line graph with a positive constant gradient indicates the acceleration is constant and the object is moving at increasing speed we can find the acceleration from V minus U / T and the distance moved is the area under the graph which is half of sum of u and v * t a straight line graph with a negative constant gradient indicator the deceleration is constant and the object is moving at decreasing speed we can find the acceleration from V minus U over T and the distance moved is the area under the graph which is half of sum of u and v * t a curved graph with an increasing gradient indicates the acceleration increases and the object is moving at increasing speed a curved graph with a decreasing gradient indicates the the acceleration decreases and the object is moving at increasing speed finding the acceleration and distance moved using velocity time graph the velocity time graph is shown here between a to B shows that the gradient is increasing so the acceleration is also increasing and the speed increases between B to C shows that the gradient is positive constant so the acceleration is also constant and the speed increases we can find the constant acceleration by the gradient of graph we draw a right triangle here is change in X or run is equal to 20 minus 7.5 is equal to 12.5 here is change in y or rise is equal to 50 - 10 is equal to 40 since the acceleration is equal to 40 / 12.5 is equal 3.2 m/s squ between C to D shows that the gradient is decreasing so the acceleration decreases and the speed increases between D to e shows that the gradient is zero so no acceleration and the speed is constant at 60 m/s between e to F shows that the gradient is negative constant so the deceleration is constant and the speed increases we can find the constant deceleration by the gradient of graph we draw a right triangle here is change in y or rise is equal to 0 - 60 = - 60 here is change in X or run is equal to 45 minus 32.5 is equal to 12.5 since the deceleration is equal to- 60 / by 12.5 = - 4.8 m/s squ we can find the average speed by the total distance moved divide by total time taken the total distance moved is equal to the area under graph the area under between a to B is approximately to area at here so we combine area under graph between a to B with area under between C to d as a rectangle since the area of this rectangle is equal to 60 * 7.5 is equal to 450 M area under graph between B to C forms a trapezium shape so it is equal to 0.5 * sum of 10 and 50 and * 12.5 is equal to 375 M area under graph between D to e to F form a trapezium shape so it is equal to 0.5 * sum of 15 and 17.5 * 60 is equal to 675 M the total area under graph is equal to 375 + 450 + 675 is equal to 1,500 the average speed is equal to 1500 divid by 45 is equal to 33.3 m/s rounded to three sign significant [Music] figures candidates are expected to have a thorough understanding of the syllabus details outlined in the accompanying figure forces force is a vector quantity that has both magnitude and Direction its unit is the Newton effects of the forces on object when forces act on an object they can cause the object to change in shape direction of moving speed forces can be categorized into two main types contact forces and non-con forces a contact force is a force that acts between two objects that are physically touching each other when two objects Collide or come into contact they exert a force on each other this force can cause a change in motion direction or shape of the objects when your hand pushes the Box a contact force propels the Box forward this is called the pushing force normal reaction force is the perpendicular force that act on an object when it is in contact with a surface when you place a box on a table the table exerts an upward Force normal force to hold the book Against Gravity tension is the force in a string spring rubber band or wire when it is stretched or compressed when you pull a box with a rope to create tension in the Rope this tension is the pulling Force transmitted through the length of the Rope friction is the force that opposes the relative motion between between two surfaces in contact when you push a box or pulling a box along the floor with a rope friction acts in the opposite direction of your applied force air or liquid resistance also known as drag force is a resistive force that acts on an object moving through air or liquid up thrust force or buoyancy force is the upward force that acts on an object that is partially or fully submerged in a fluid a non-contact force is a force that acts between two objects that are not physically touching non-con forces act through a field which is an invisible region of space that surrounds an object and exerts a force on other objects within that field the gravitational force or weight due to the gravitational field strength of Earth its direction is always downward Earth's gravity pulls objects to towards its Center even without touching them we can calculate the weight of the object using the equation W equals mg where W is weight in Newtons m is mass in kilogram and G is gravitational field strength in Newtons per kilogram electrostatic force is the force between the charged objects charged objects attract or repel each other depending on their charges and distance between them like charges repel unlike charges attract magnetic force is the force between the magnets magnets attract or repel each other without physical contact like poles repel unlike poles attract when a car is moving to the right as shown there are the forces acting on a car including the weight acts downward the total normal reaction ction forces is acting Upward at its Wheels the force from the engine acting forward the air resistance acting backward when a box is at rest on a rough incline as shown there are the forces acting on a box including the weight acts downward the normal reaction force acts upward perpendicular to the slope the friction acts upward parallel to the slope when we pull a box with a rope along the incline causing the box to move up the incline there are forces acting on the box including the tension acts up along the slope the friction acts downward parallel to the slope because the box is moving up the slope the weight acts downward the normal reaction force acts upward perpendicular to the slope when a box floats on the water there are forces acting on the box including the weight acts downward the up thrust acts upward when a metal sphere is moving downward through the water there are forces acting on the metal including the weight acts downward the up thrust acts upward the water resistance acts upward resultant Force the resultant force or net force is the single force that has the same effect as all the other forces forces acting on an object combined if the resultant force is zero it is called balance force if the resultant force is not zero it is called unbalanced force we can find the resultant force that acting on the object for example a box a has forces acting on it as shown the forces on the left and right sides of the Box are balanced this means the net force acting on the box in the horizontal direction is is zero in the vertical Direction there is a resultant force of 8 Newtons acting downwards this can be found by subtracting the downward Force 22 Newtons from the upward Force 14 Newtons a box B has the forces acting on it as shown the resultant force acting on the object is 360 Newtons to the right this can be determined by adding the two forces acting to the right 300 Newtons and 60 newtons a box C has the forces acting on it as shown there is a resultant force of one newton acting to the right this can be found by adding the two rightward forces two Newtons and four Newtons and subtracting the leftward force five Newtons a box D has the forces acting on it as shown there is a resultant force of 170 Newtons acting to the right this can be found by subtracting the rightward force of 200 Newtons and the leftward force 30 Newtons the three laws of motion also known as Newton's Laws of Motion Newton's first law of motion the forces on an object are all balanced then it will just stay still or else it is already moving it will just carry on at the constant velocity when a car is at rest then the forces on it must be balanced so car's weight acts downward to equal the total normal forces acting upward when you pushes a car with a force 500 Newtons to the right and a car stay still this causes the total friction between the tires and the road's surface to act to the left 500 Newtons for balancing with the pushing force when a car is moving with constant velocity then the forces on it must be balanced so car's weight acts downward to equal the total normal forces acting upward the force from engine 2,500 Newtons acting forward is balanced with the fair resistance 2,500 Newtons acting backward when a ball is falling down with constant velocity then the forces on it must be balanced the downward weight 10 Newtons is balanced with the total upward up thrust 1 Newton and air resistance 9 Newtons since we can conclude that when no resultant force or balanced force the object is stationary or moving with constant velocity and its acceleration is zero Newton's second law of motion if there is a resultant Force unbalanced force then the object will accelerate in that direction this acceleration can be done by changing the object object's velocity the change in velocity caused the object to start speeding up slowing down stop and changing direction if a resultant Force acts on an object at rest the object will accelerate starting to move increasing its speed if a resultant Force acts on an object in the opposite direction of its motion the object will decelerate eventually coming to a stop if a resultant Force acts on an object in the same direction direction of its motion the object will accelerate further increasing its speed if a resultant Force acts on an object at a perpendicular angle to its direction of motion the object will change direction while its speed Remains the Same the acceleration of an object is directly proportional to the resultant Force the bigger the force the greater the acceleration the acceleration is inversely proportion to mass of the object the bigger the mass the smaller the acceleration this can be expressed mathematically as F equal m a where f is the resultant force in Newtons m is the mass in kilogram a is the acceleration in m/s squared for example find the resultant force and acceleration of the box with magnitude and Direction like as shown the resultant force is the subtracting the leftward force 15 Newtons with the rightward force is 4 Newtons and 2 Newtons resulting 9 Newtons to the left calculate the acceleration using f = m a substitute F = 9 Newtons Mass equal 2 kg then a = 9 / 2 is equal to 4.5 m/s squar to the left Newton's third law of motion when object a exerts a force on object B then object B exerts an equal an opposite force on object a a pair of forces must be equal in magnitude opposite in direction and act on different objects for example a book lying on a table exerts a downward force on the table this is the action force the table also exerts an equal an opposite force on the book in the upward Direction this is the reaction force the Earth exerts a downward force on the book this is the action force the book also exerts an equal and opposite force on the earth in the upward Direction This is the reaction force while moving on the ground we push the ground backward with our feet this is the action force the ground also exerts a forward force on our feet of equal magnitude in the opposite direction which makes us move forward this is the reaction force a man's hand exerts a force on the wall this is the action force the wall also exerts an equal an opposite force on a man's hand in the backward Force this is the reaction force a rocket exerts a downward force on the burnt gases this is the action force the burnt gases also exerts an equal an opposite force on the rocket in an upward Direction This is the reaction force stopping distance is the distance a vehicle travels from the moment the brakes are applied to the moment it comes to a complete stop if a car is traveling at a constant speed U and the driver suddenly sees a cow they will apply the brakes to bring the car to a complete stop the distance between the point where the driver sees the C and the point where they apply the brakes is called the reaction distance or thinking distance the distance traveled by the car from the moment the brakes are applied until it comes to a complete stop is called the braking distance the total stopping distance is the sum of the reaction distance and the breaking distance we can represent the stopping distance visually using a velocity time graph as shown this time T1 represents the driver's reaction time the gradient of this section represents the car's constant deceleration due to the brakes this area under the graph is the reaction or thinking distance which is U T1 this area under the graph is the breaking distance which is half of U * T2 minus T1 therefore the stopping distance is equal to U T1 + half of U * T 2 - t one the factors affecting the vehicle stopping distance include vehicle speed higher speeds result in significantly longer stopping distances which affects both reaction distance and braking distance vehicle Mass a heavier vehicle has a longer braking distance because it requires more Force to decelerate road conditions wet icy or uneven roads can extend braking distance by reducing the friction between the tires and the road surface reaction time the time it takes for driver to react to danger and apply the brakes results in the reaction distance so higher Reaction Time higher the reaction distance factors affecting the reaction time include driver age Reaction Time generally increases with age intoxication alcohol or drugs significantly increases reaction time fatigue being tired significantly increases Reaction Time braking efficiency the condition of your vehicle's Brakes and Tires directly affects its ability to slow down this affects the braking distance Free Fall is the motion of an object under the influence of gravity only if a feather and a bowling ball are dropped at the same time from the same position in air the B rolling ball will reach the ground first this happens because air resistance has a greater effect on the feather due to its larger surface area if a feather and a bowling ball are dropped at the same time from the same position in a vacuum they will reach the ground at same time and same speed this is because air resistance has no effect on them this is called Free Fall that applies to all objects regardless of their mass in a vacuum Free Fall describes the motion of an object under the influence of gravity only we can conclude that there is no air resistance and only weight acting on the object the object accelerates constantly towards the ground due to gravity this acceleration is typically denoted by the symbol G and has a value of approximately 10 m/s squared when a ball is moving as free fall its velocity increases by 10 m/s every second this is because its acceleration is approximately constant at 10 m/s squared a ball is dropped at rest its initial velocity is zero and its initial acceleration is 10 m/s squared after 1 second the ball has descended and its velocity increases from 0 to 10 m/s after 2 seconds the ball has descended a greater distance than it did first second and its velocity increases to 20 m/s after 3 seconds the ball has descended a greater distance than it did between 1 and 2 seconds and its velocity increases to 30 m/s after 4 seconds the ball has descended a greater distance than it did between 2 and 3 seconds and its velocity at 4 seconds increases to 40 m/s the velocity time graph of a free fall the velocity of a ball increases 10 m/s every second therefore we plot the graph with the following points Time 1 second velocity is 10 time 2 seconds velocity is 20 time 3 seconds velocity is 30 Time 4 seconds velocity is 40 then we draw a straight line from the origin the velocity time graph shows that the gradient is constant which indicates that velocity increases with constant acceleration of 10 m/s squared we can find the distance moved of the ball from the area under the graph distance moved between 0 and 1 second equals 05 * 1 te 10 is equal to 5 m distance moved between 1 and 2 seconds equals 0.5 * sum of 10 and 20 and * 1 is equal to 15 m distance moved between 2 and 3 seconds equals 0.5 * sum of 20 and 30 and * 1 is equal to 25 M distance moved between 3 and 4 seconds equals 0.5 * sum of 30 and 40 and * 1 is equal to 35 M you see that the distance moved of a ball increases for 10 m every second the distance time graph of a free fall we can plot the graph at 1 second the distance 5 m at 2 seconds the distance is 15 + 5 is equal to 20 M at 3 seconds the distance is 20 + 25 is equal to 45 M at 4 seconds the distance is 45 + 35 is equal to 80 M then we draw a best fit curve from the distance time graph shows that the gradient is increasing which indicates that the velocity is also increasing with constant acceleration of 10 m/s squared terminal velocity is the maximum speed an object reaches when moving through a fluid liquid or gas due to the balance forces no resultant Force when an object is moving through a fluid there is a drag force due to the fluid this drag Force can increase when the speed of the object increases and the surface area of the object increases right now we will use the symbol of Sigma F to represent the resultant Force consider the terminal velocity of a sky diver when a sky diver jumps out of airplane they are initially at rest drag force is zero because their speed is zero only weight acts on them downward so the resultant force is equal to their weight since their initial acceleration is 10 m/s squared this cause their speed to increas is from zero and the drag Force also increases as time passes drag Force acts upward to increase as speed increases the resultant force is equal to their weight minus drag Force which acts downward to decrease this causes their acceleration also decreases as drag Force increases until it equals their weight this causes the resultant force is zero since their acceleration also is zero this causes their speed is constant this is called terminal velocity when a parachute is opened the large surface area increases the drag Force to act upward this causes the resultant force to be drag Force minus their weight which acts upward since the acceleration is also upwards so the sky diver decelerates and their speed decreases as time is passes the drag Force acts upward to decrease as speed decreases since the resultant Force acts upward to decrease and their deceleration also decreases as the drag Force decreases until it equals their weight so the resultant force is zero this causes their acceleration is also zero and their speed is constant again this speed is called terminal velocity the velocity time graph of the skydiver's motion is shown on the screen we known that the gradient of velocity time graph is the acceleration at Point a initial velocity is zero and initial gradient is 10 this is because the initial acceleration is 10 m/s squared between points A and B the gradient decreases this means that the acceleration also decreases while the velocity still increases between B and C the velocity is constant and this velocity is called terminal velocity the gradient of graph is zero this means that the acceleration is also zero at Point C the parachute is opened large surface area of the parachute causing large drag Force this causes the velocity to decrease as rapidly between C and D the velocity decreases the gradient is negative so the parachutist decelerates the steepness of the gradient decreases so the deceleration also decreases between d and e the velocity is constant which is terminal velocity the gradient is zero this means that the acceleration is also zero the parachutist reaches the ground at Point e the velocity time graph showing the difference between free fall and terminal velocity of a ball when a ball falls through a vacuum there is no air resistance acting on it this is called Free Fall the velocity time graph of this scenario is a straight line passing through the origin the constant gradient represents the ball's constant acceleration due to gravity which is around 10 m/s squared this is because only any force acting on the ball is its weight acting downwards so the resultant force is the weight when a ball falls through air there is air resistance acting on it the velocity time graph of this scenario is a curve with a decreasing gradient that eventually becomes horizontal the initial gradient is around 10 m/s squared represents the ball's acceleration due to gravity this is because at the beginning the only force acting on the ball is its way acting downwards making the weight the initial resultant force over time the decreasing gradient of the graph shows that the acceleration of the ball decreases this is because as the ball Falls faster air resistance also increases this air resistance acts in the upward Direction opposing the weight so the resultant force is the weight minus the air resistance becomes smaller as air resistance increases when the grade I reaches zero it indicates that the acceleration is also zero this causes the velocity of the ball is constant and reaches its terminal velocity at terminal velocity the air resistance acting upwards is equal to the weight acting downwards since the resultant force is zero a ball falling through air will take longer and reach the ground at a slower speed compared to a ball falling through a vacuum from the same height deformation of material investigate how extension varies with applied force for helical Springs set up the apparatus as shown measure the original length of the unstretched spring using a ruler hang a Load One North on the spring and then measure the length of the spring calculate the extension by subtracting the length from the original length repeat the experiment for addition loads of 2 Newtons 3 Newtons 4 Newtons 5 Newtons and 6 Newtons record the results of the length of the spring and its extension in the table plot the graph of the load in Newtons against the extension in centimet as shown we can conclude the results from the graph as follows here the result is a straight line graph passing through the origin of the axis this shows that the spring obeys hooks law hook law states the extension of the spring string or wire is directly proportional to the force or load in this region the spring is not a Baye hooks law at this point is called the limit of proportionality it is the point where the spring stops obeying hooks law and starts to stretch more for each increase in the load Force at this point is called the elastic limit if the spring is stretched Beyond its elastic limit it will not return to its original length when when the weights are removed investigate how extension varies with applied force for elastic bands we set up the apparatus as shown to investigate how an elastic band stretches under load if you stretch an elastic band with increasing load forces we get a graph of load against extension like as shown the graph is not a straight line showing that elastic bands do not obey hooks law if the graph of load against extension of material when it loaded and unloaded like as shown this shows that this material stretches elastically this is called elastic deformation this means that a wire spring or rubber band that stretches elastically will return to its original length once the stretching force is removed if the graph of load against extension of material when it loaded and unloaded like as shown this shows that this material stretches plastically this is called plastic deformation this means that a wire spring or rubber band that stretches plastically will not return to its original length once the stretching force is removed momentum is a measure of the tendency of an object to keep moving or of how hard it is to stop it moving momentum is defined as the product of mass and velocity we can write the equation of the momentum as P equal MV where p is momentum in Newton Second or kilog m/s M is mass in kilog V is the velocity in m/s momentum is a vector quantity due to the velocity is Vector so the direction of momentum is same as the direction of velocity for example a 1200 kg car is stationary so its momentum is zero this is because its velocity is zero when this car is moving with 25 m/s its momentum is 1,200 * 25 is equal to 30,000 kg m/s the same car is moving and it has momentum of 45,000 kg m/s to find the car's velocity we can substitute P = 45,000 kg m/s and equal 1,200 kg so its velocity is 45,000 / 1,200 is equal to 37.5 m/s momentum Newton's second law of motion and acceleration from Newton's second law of motion f equals m a from the acceleration of the object the equals vus U / T we combine two equations together as we get f = m vus m u / T this is the change in momentum per unit time we can conclude that the resultant force is the rate of change in momentum we can write the equation as shown where f is the resultant force in Newton MV is final momentum mu U is initial momentum T is time in second first example A2000 kg car accelerates from 10 m/s to 25 m/s in 10 seconds what resultant Force produced this acceleration we substitute m is 2,000 kg V is 25 m/s U is 10 m/s and T is 10 seconds so the result of force is 3,000 Newtons second example the first stage of the type of Rocket used in Moon missions provides an unbalanced upward away from the earth force of 30 Mega Newtons and burns for 2.5 minutes calculate the increase in the Rockets momentum that results convert 30 megga Newtons into Newtons it is 30 * 10 the^ of 6 Newtons convert 2.5 minutes into seconds it is 2.5 * 60 is equal to 150 seconds change in momentum is m vus m u = ft so increase in momentum equals 30 * 10 ^ 6 * 150 is equal to 4.5 * 10 ^ of 9 kg m/ second if the rocket has a mass of 3,000 ton what is the velocity of the rocket after the first stage has completed its burn convert 3,000 tones into kilog it is 3,000 * 1,000 is equal to 3 * 10 ^ of 6 kg the rocket starts from rest so U equal 0 and then mu U equal 0 increase in momentum equals m v substitute the increase in momentum equal 4.5 * 10 ^ of 9 and m = 3 * 10 ^ 6 so V = 1,500 m/s momentum in Collision the total momentum of objects that Collide Remains the Same this is called the conservation of momentum since total momentum of the system before Collision is equal to the total momentum of the system after Collision let's consider a moving ball a with mass M1 rolls towards stationary Ball B with mass M2 so total momentum before Collision is M1 U the balls after the Collision have the velocities as shown so total momentum after Collision is M1 V1 plus M2 V2 during the impact each ball exerts a force on the other with equal in size and opposite in direction this is because Newton's three law about action and reaction as shown the forces act each ball for the same amount of time this means that f * t for each is the same size but opposite in direction since the change in momentum of ball a is equal in size but opposite direction with the change in momentum of Ball B so total momentum before Collision is equal to total momentum after Collision for example find the speed of ball after the Collision like as shown we given the sign of velocity's direction to the right is positive and to the left is negative the total momentum before Collision is the sum of ball A's momentum and balls B momentum which is 0.4 * 2.5 + 0.6 * - 1.2 it is equal to 0.28 kg m/s the total momentum after Collision is 0.4 * - 0.5 + 0.6 * V it is equal to - 0.2 + 0.6 EV kg m/s the total momentum before Collision is equal to the total momentum after collision and then V is 0.8 m/s to the right due to the positive sign therefore speed of Ball B after Collision is 0.8 m/s momentum in explosion the conservation of momentum principle can be applied to explosions the total momentum of the system before the explosion is equal to the total momentum of the system after the explosion although there will be a significant increase in the total kinetic energy of the fragments an explosion involves a rapid release of energy causing an object to break apart into pieces that fly in different directions let's consider an object with mass m that is stationary before the explosion so its momentum is zero the object explodes into two fragments with masses M1 and M2 which move apart at velocities V1 and V2 respectively the total momentum after the explosion is the sum of the momenta of the two fragments M1 V1 + M2 V2 momentum is conserved when during explosion so total momentum before explosion equals total momentum after explosion then 0 equal M1 V1 + M2 V2 and M1 V1 equal minus M2 V2 this equation tells us that the momentum of fragment M1 is equal in magnitude but opposite in direction to the momentum of fragment M2 as the rocket Burns the fuel generating hot gases that are ejected at high speeds from the rocket this produces the momentum large amount of fast moving gases out of the back of the rocket so the rocket gains an equal amount of momentum in the opposite direction to that of the moving exhaust gases momentum in safety car a larger Force means a faster change of momentum and so greater acceleration likewise if someone's momentum changes very quickly like in a car crash the forces on the body will be very large and more likely to cause injury cars are now designed with various safety features that increase the time over which the car's momentum changes in an accident crumple zones airbags and seat belts in a car increase the Collision time crumple zones on impact increasing the impact time taken for the car to stop airbags slow you down more gradually increasing the impact time this reduces the force acting on the body seat belts stretch slightly increasing the time taken for the wearer to stop this reduces the forces acting on the chest for example a car traveling at 20 m/s collides with a wall and is brought to rest in just 0.02 seconds a man in the car has a mass of 50 kg he experiences the same deceleration when he comes into contact with a hard surface in the car such as the dashboard or the wind screen what force does the person experience to find the force acting on the person by this equation we substitute m is 50 kg V is 0 m/s U is 20 m/ second and T is 0.02 seconds so the resultant force is 50,000 Newtons turning effect of forces is a measure of the moment forces when forces act around a fixed Point called a pivot they have turning effects called moments we use these effects all the time in everyday life for some everyday examples as a spanner or wrench uses to loosen a nut you apply a force that creates an anticlockwise moment helping you turn the nut a claw hammer uses to remove a nail the force applied on the handle to create the moment of force a scissors work by applying two opposing forces that create a moment causing the blades to come together and cut through material a seil pivots on a central point and the moment created by children sitting on either end determines its clockwise or anticlockwise movement a lver is tools that utilize the concept of moment of force to simplify the applied force making it easier to lift or move heavy objects a door is opened by pushing or pulling on a door knob you create a moment of force that causes the door to rotate on its hinges a wheelbarrow distributes the weight of a heavy object allowing you to apply a smaller Force at the handles to move it with a larger moment steering wheels of a car is turned to create a moment that alters the direction of the wheels ultimately controlling the car's Direction moment of forces is defined as the product of force and perpendicular distance between line of action and pivot we can write the equation as m equal f d where m is the moment of force in Newton meter f is force in Newtons D is perpendicular distance from pivot in meters for first example A4 Newton's Force acts on the light white Beam at a perpendicular distance of 3 m from the pivot this causes the clockwise moment to be 3 * 4 is equal to 12 Newton M about the pivot second example A3 Newton's Force acts on the light beam at a perpendicular distance of 2 m from the pivot this causes the anticlockwise moment to be 3 * 2 is equal to 6 Newton M about the pivot third example A4 Newton Force acts at the end of beam along pivot as shown this causes the moment is zero due to the force acting along the pivot causing perpendicular distance from pivot to be zero fourth example A5 Newton's Force acts at the end of beam and 2 m perpendicular distance between line of action and pivot this causes the anticlockwise moment to be 5 * 2 is equal to 10 Newton M about the pivot fifth example a diagram shows the forces acting on a light beam and distance of each force from point P calculate the sum or resultant moment about P clockwise moment about P causes by forces 3 Newtons 1 M from p and 4 Newtons 3 m from P so total clockwise moment equals 4 * 3 + 3 * 1 is equal to 15 Newtons M anticlockwise moment about P causes by only 2 Newtons 1 M from P so anticlockwise moment equal 2 * 1 is equal to 2 Newtons M you see that larger total clockwise moment than clockwise moment so the resultant moment equals 15 - 2 is equal to 13 Newt m in clockwise the principle of moment states that if an object is in equilibrium the total of clockwise moment is equal to the total anticlockwise moment about the pivot the conditions for equilibrium of an object are there is no resultant force acting on the object there is no resultant moment acting on the object this is the principle of moment for example someone is trying to balance a plank with particles A and B the plank has negligible weight calculate the moment of the forces about Point O and determine if the plank will balance if not calculate the force acting on the plank at P calculate the moment of four newon Force about point0 which is 4 * 4 is equal to 16 Newton m in clockwise calculate the moment of 6 Newtons Force about Point O which is 2 * 6 is equal to 12 Newt m in anticlockwise since the clockwise moment is greater than the anticlockwise moment the plank will rotate clockwise resultant moment equal 16 - 12 is equal to 4 Newtons M to balance the plank we need to add an additional downward Force at Point P that will create anticlockwise moment of 4 Newton M perpendicular distance between point P to Pivot o is 4 M so Force FAL 4 / 4 is equal to 1 Newton therefore the plank will balance if a force of 1 Newton is applied downward at Point P center of gravity the center of gravity is sometimes called the center of mass it is the point where the whole of the weight of the object appears to act the weight of all object acts through the center of gravity for example the center of gravity of the human is about here the center of gravity of an apple is about here the center of gravity of a magnet is here a uniform object's center of gravity is at the middle of the object for example a uniform cylinder has its center of gravity at here a uniform sphere has its center of gravity at the center a uniform Cube has its center of gravity at here a uniform wooden meter rule has its center of gravity at the 50 cm Mark the the object will always balance around its center of gravity for example the wooden meter rule is balancing on the pivot at the 50 cm Mark like as shown you can try balancing a pencil on your finger like as shown the people is walking on the Rope like as shows someone of weight 500 Newtons is standing on a uniform plank 6 M long and weighing 250 Newtons the plank is supported by two trestles as shown calculate that the upward force is X and Y exerted by the trestles on the plank the plank is uniform so the center of gravity is the middle of the plank equals 2.5 M from Trestle y the plank is equilibrium because it is at rest and not turning so the principle of moments can be applied finding X let's take Trestle y as the pivot the total clockwise moment about y equals the total anticlockwise moment about y total clockwise moment 5 * X and equal to Total anticlockwise moment 500 * 3 + 250 * 2.5 we will get 5x = 2125 so x = 425 Newtons finding why using total upward force on the plank equals total downward force on the plank because no resultant Force acts on the plank total upward force is 425 plus y equals total downward force is 500 + 250 so y = 325 Newtons a diagram shows an arm with the hand holding a weight of 120 Newtons the 20 newtons force is the weight of the forearm acting at the center of gravity f is the force in the muscle of the upper arm p is the point in the elbow about which the arm pivots the distances of the forces from point P are shown by taking moments about Point P calculate the force f a diagram shows an arm is equilibrium or balance so total clockwise moment equals total anticlockwise moment total clockwise moment causes by 20 newtons Force 15 cm from p and 120 Newtons Force 33 cm from P so total clockwise moment is 20 * 15 + 120 * 33 is equal to 4,260 newtons M total anticlockwise moment is force f * 2 therefore Force f is 4,260 / 2 is equal to 2,130 newtons a force acts on the forearm at Point P calculate this force and state its direction we can apply the total upward acting on arm equals total downward force acting on arm due to equilibrium of arm total upward Force equals 2,130 Newtons to total downward force equal 20 + 140 is equal to 140 Newtons total upward force is more than total downward Force to balance the arm we need to add an additional downward Force at Point P the magnitude of this Force equals 2,130 - 140 is equal to 1,990 newtons I hope you found this video helpful if you did I would be grateful if you would subscribe share like and leave a positive comment your support will encourage me to create more content thank you