Find acceleration

Question

A mass is being pulled up an incline plane. The angle of the incline plane is 33 degrees. The mass is 11 kg and the pulling force is 185 N at an angle of 25 degrees to the plane. The coefficient of friction is 0.44, what is the acceleration?

Answer 1

The key to this one is drawing out (or, in the absence of a white board, thinking out) the force diagram.  First in the y-axis (perpendicular to the incline), we have

 

F_gy = 11 kg * 9.8 m/s2 * cos(33) = -90.4 N

F_N = F_gy = 90.4 N  (since the mass isn't sinking into or rising out of the plane)

 

In the x-axis (parallel to the incline), we have:

 

Pulling Force: 185N

F_fr =  -0.44*90.4N = -39.8 N   (negative because friction opposes the pulling force)

F_gx = 11 kg * 9.8 m/s2 * sin(33) = -58.7 N

 

So, ∑Fx = 185 - 39.8 - 58.7 = 86.5N

 

Therefore, a = F/m = 86.5N / 11kg = 7.86 m/s².