[Music] hi and welcome back to three sites lessons.com okay by the end of this video you should be able to use a vector diagram to resolve a single force into two forces and this is for higher-tier students only in the last video we saw how to use a vector diagram to work out the resultant of two forces acting at an angle in this video we're going to use vector diagrams again but in this case we're going to take a single force and resolve it into two components in other words two parts again this can look tricky but it really isn't once you get the idea I'm showing you here a horizontal force as you can see all of this force is acting in the horizontal direction no part of this force is acting in the vertical direction this shows a vertical force in this case all of this force is acting in the vertical direction and no part of the force is acting in the horizontal direction this force is acting diagonally what that means is that part of the force is acting horizontally in other words in the x-direction and part of the force is acting vertically in other words in the y-direction I'm going to show that by putting x and y-axes on the diagram like this so this shows the horizontal component of the force and this shows that the vertical component of the force so we've taken a single force and resolved it into two components and these two components must be at right angles to each other now we can do this for any force and if we draw a vector diagram to scale we can determine the magnitude of the horizontal and the vertical components here's a typical question a 100 Newton force is acting at an angle of 35 degrees with the horizontal determine the horizontal and vertical components of this force so to answer this question we draw a scale a vector diagram of the force we're going to use a scale of 1 centimeter equals 10 Newtons here's the object that the force is acting on first we draw faint lines to show the horizontal and vertical axes using a protractor we measure 35 degrees from the horizontal we now use a ruler to draw the vector showing the 100 Newton force in this case the vector will have a length of 10 centimeters now we draw dotted lines from the head of the vector to the horizontal and vertical axes at this point we can draw a horizontal and vertical components like this finally we use a ruler to determine their magnitude the horizontal component has a length of eight point three centimeters and the vertical component has a length of five point seven centimeters that means that the horizontal component has a magnitude of 83 Newtons and the vertical component has a magnitude of 57 Newtons I should point out in the exam it's a good idea to blob out any of the faint lines that you've used so that you only show the vectors in the final answer okay here's a question for you to try is 75 Newton force is acting at an angle of 20 degrees with the horizontal determine the horizontal and vertical components of this force so pause the video now and try this yourself okay I'm using a scale of 1 centimeter equals 10 Newtons so here's a vector diagram we now draw dotted lines from the head of the vector to the horizontal and vertical axes like this and then we draw a horizontal and vertical components finally we measure the lengths of these components undetermined Amarna two'd the horizontal component has a length of 7 centimeters so this represents 70 Newtons and the vertical component has a length of 2.5 centimeters so this represents 25 Newtons find plenty of questions on resolving forces in my vision workbook and you can get that by clicking on the link above [Music]