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Math question please help

hi. how can two horizontal forces have an angle of 60 degrees? Also how would i go about drawing the graph? Also, i checked the solutions for part i and they used the cosine rule to find the magnitude which is fine expect they used cos120 instead of cos60, what? i don't understand? i'm on the verge of a mental breakdown and my pure and mechanics exam is tomorrow. Please help me. Thank you very much.

Reply 1

Squirmz

I think it means in 3D, like if you put 2 pencils on a table touching at one end with a 60° angle between them and pushed something with that end... It is slightly ambiguous though i’ll give you that

Reply 2

nzy

By 'graph' I assume you mean a force diagram. If two forces are both horizontal, that means they're just in the same plane (rather than facing the same direction). For this situation, that would simply look like this (excuse the poor MS paint drawing):

For part i), using cos60 for the cosine rule would give you the magnitude of the opposite side of the triangle (black dashed line below), which is not the same as resultant of the two forces.

In order to find the resultant using a diagram, you need to draw one of the forces after the other (i.e. from the starting point, draw one of the arrows, and then, starting from the tip of that arrow, draw the second arrow). Another way to approach this is to draw a parallelogram of forces (completed in grey), and where the resultant force R is equal to the diagonal (grey dashed line)