Thread: Velocity as a function of time

Please explain how to interpret this graph as well as the rest of the problem. Thank you!



Two horizontal forces 1 and 2 act on a 3.0 kg disk that slides over frictionless ice, on which an xy coordinate system is laid out. Force 1 is in the positive direction of the x axis and has a magnitude of 6.7 N. Force 2 has a magnitude of 9.0 N. Figure 5-34 gives the x component vx of the velocity of the disk as a function of time t during the sliding. What is the angle between the constant directions of forces 1 and 2?
Fig. 5-34
Problem 12.

This problem asks to to relate kinematics (motion) and dynamics (forces). This should instantly make you think Fnet=m*a. Mainily we are woried about the x component, though, so we'll say Fnet_x = m*a_x.

Now, you should know, that acceleration is a derivative of velocity, and that on a graph, the derivative is the slope. so a = dv/dx = rise/run = 6/2 = 3 m/s^2.

now, we have a mass of 3.0 kg, and an acceleration of 3m/s^2, so Fnet_x = 3*3 = 9N.

now, its a matter of adding the forces:
Fnet_x = F1_x + F2_x

F1 is along the X axis:
F1_x = F1 = 6.7N
F2 is not so we multiply its magnitude by cos(theta):
F2_x = F2*cos(th) = 9N*cos(th)
and we already know:
Fnet_x = 9N

we plug these back into the above equation:
9N = 6.7N + 9N*cos(theta)

now its an algebra problem:
9N*cos(th) = 9N - 6.7N = 2.3N
cos(theta) = 2.3N/9N = .255555555555
theta = arccos(.255555555555) = 75.19 degrees