resolving inclined forces hello everyone and welcome back to our Channel today we will learn how to resolve inclined forces why do we need to resolve inclined forces before we dive into the process let's understand why resolving inclined forces is necessary in engineering whenever multiple forces are acting on a body or system we need to determine the resultant Force this resultant force shows us the combined effect of all the forces and the direction in which they will move the body by understanding the resultant Force we can apply an equal and opposite Force known as a counter Force to keep the system stable this is crucial in designing and analyzing structures machinery and various mechanical systems to ensure they function safely and effectively why can't we add forces directly you might wonder why we can't simp add forces acting on a body directly the reason is that forces are vector quantities which means they have both magnitude and direction to add multiple forces correctly we need to consider both these aspects suppose two forces are acting in different directions if we add these forces directly without considering their directions the resulting force would be incorrect when one force acts opposite to another they oppose each other and the stronger force will determine determine the direction of the resultant Force adding forces acting vertically and horizontally is straightforward we consider the XY plane where forces acting to the right are positive and those to the left are negative similarly forces acting upward are positive and those acting downward are negative this convention remains consistent regardless of the placement of the forces as long as they are in vertical or horizontal directions however if a force acts in a random Direction on this plane we need to resolve it resolving a force means breaking it down into its vertical and horizontal components for instance if a 10 Newton Force acts at an angle we find out how much of that 10 Newtons acts vertically and how much acts horizontally let's understand this with an example imagine there is a square on this plane if a force acts at a point on the Square in a specific Direction it will cause the square to move in that direction the same effect can be created with two forces one acting from the left moving the square horizontally and another acting from the bottom moving it vertically together these two forces will cause the square to move in the same direction as the original single force in this scenario the two forces acting from the left and bottom are the components of the original Force therefore whenever we want to add two different incline forces we first resolve them into their horizontal and vertical components once resolved we can easily add the corresponding components together to find the resultant Force let's start with resolving a single Force suppose a 20 K force is acting at a 40° inclination as shown to resolve the force into its components we need two pieces of information the magnetude of the force which is 20 K in this case and the direction of the force which is a 40° inclination with the horizontal with this information we can easily find the components of the force to find the horizontal component of the force we multiply force f with cosine Theta this is the general form here Theta is the angle made by the force with the horizontal therefore the horizontal component of the force which we denote as FX will be equal to 20 * the cosine of 40° after after calculating we get 15.32% iCal component FY is equal to 12.86 K key points to remember here if the force makes an angle with the horizontal to find the horizontal component we multiply that force with the cosine of the angle made for example consider another situation if instead of a 40° angle with the horizontal we had a 50° angle with the vertical these two figures are exactly the same in this case to find the horizontal component of the force we have to multiply force f with the sign of the angle 50° on the other hand to find the vertical component of the force we multiply force f with the cosine of angle 50° in both examples we will get the final values of the horizontal and vertical components to be the same therefore it's very important to see where the angle is provided based on that we should decide whether to multiply the force with cosine or sign to get the required component I hope this clarifies when we should use cosine and when we should use S next we will take a complex example to enhance our understanding we're looking at a concurrent Force system in a concurrent Force system the lines of action of all the forces intersect at a single point in this scenario we can observe various forces acting through a single point for such problems we typically need to determine three things the resultant Force the direction of the resultant force and the position of the resultant Force let's start resolving to fund the resultant Force we need to get the summation of horizontal forces in this system and the summation of vertical forces we can see this 30 Newton force is acting horizontally therefore there is no vertical component for this Force similarly this 50 Newton force is acting in vertical Direction therefore there is no horizontal component in this Force apart from these two forces we have these three inclin forces these inclin forces have vertical and horizontal components let's mark these two components for each of the forces consider this 80 Newton Force we can see this force is acting away from the center point therefore the vertical and horizontal components of this Force also act away from the center next this 50 Newton Force we can see it is acting towards the center there therefore the components of this Force also act towards the center and this 120 newton Force this force is acting away from the center so therefore its components will also act away from the center as shown therefore we have all the component forces marked now let's calculate the forces for each component consider this 80 Newton Force its horizontal component will be 80 cosine 30° the vertical component will be 80 sin 30° if the angle made by the force is a horizontal component then horizontal component is given as force that is 80 Newton multiplied by cosine of angle made in this case the angle made is 30° next consider this 50 Newton Force the angle made by the force with the horizontal component is 60° therefore the horizontal component is given as a force that is 50 Newton multiplied by a cosine of 60° the vertical component is given by 50 Newton multiplied by a s of 60° in the end consider this 120 newton Force horizontal component is given by 120 newton multiplied by cine of 65° and the vertical force is given by 120 newton multiplied by a s of 65° therefore we have all the vertical and the horizontal forces now we need to do the of all the horizontal forces and the vertical forces let's do the summation of horizontal forces while summing up the horizontal forces we consider all the forces acting to the right as positive and all the forces acting to the left as negative we can see that this 30 Newtons force is acting to the right next this 80 cosine 30° is acting to the right this 50 cosine 60° is acting to the right and this 120 cosine 65° is acting to the left so this force will have a negative sign when we calculate these forces we get these values the summation of all these forces will be equal to 73.5 S Newtons next we will do the summation of vertical forces while summing up the vertical forces we consider all the forces acting upward as positive and all the forces acting downward as negative therefore we have this Force 80 sin 30° acting in the upward direction as positive next this Force 50 sin 60° is acting in the downward direction as negative next this 120 sin 65° is acting in a downward direction as negative and this 50 Newtons force is acting in the upward direction as positive when we solve for these forces we get these values the summation of all these forces will be - 62.5 Newtons therefore we have the summation of horizontal and vertical forces with this we can find the resultant force of the system the resultant force is given by r equal to square root of summation of horizontal forces square plus summation of vertical forces Square here substitute the values of the summation of horizontal forces which is 7357 squ plus the summation of vertical forces which is - 62.5 Square the resultant force will be 96.24 Newtons next we will find the direction of the resultant Force the direction in other words the angle made by the resultant Force Theta is given by the tan inverse of the absolute value of the summation of vertical forces divided by the summation of horizontal forces substitute the values of the summation of vertical forces which is 62.0 divided by the summation of horizontal forces which is 7357 after solving we get the angle Theta equal to 40.1 4° next we need to show the position of the resultant Force the position of the resultant Force depends on the direction of the summation of the horizontal and vertical forces in our case the summation of horizontal forces is positive 73.5 7 Newtons here positive means the direction of the horizontal Force is to the right side similarly the summation of vertical forces is - 62.5 Newtons the negative sign shows the net force acting towards the downward side therefore if we consider a point our summation of horizontal force is acting to the right from this point and our summation of vertical force is acting downward from this point by joining the end points of the forces we can create a rectangle here our result force will act like this making an angle of 40.1 4° remember the length of these horizontal and vertical forces should be approximately proportional to their magnitudes therefore we have the position of the resultant Force according to this our resultant force is in the fourth quadrant I hope this video helps you understand how to resolve forces into their components find the resultant force and determine its direction and position if you like this video click on the like button and if you are new to my channel ADW study click on the Subscribe button to get all my latest videos