A mass of 7 kg is placed on an incline with friction and no additional forces ac

Question

A mass of 7 kg is placed on an incline with friction and no additional forces acting on it and it begins to slide at some angle when the angle is slowly increased as discussed in class. Now, the same mass is placed on the same incline, but an additional force of 22 Newtons is applied to it perpendicular from the incline, away from the incline (it's always in that direction). As the angle of the incline is slowly increased, it slides at a different angle with this force. If the angle which it begins to slide with the force is 33 degrees, how much further can the angle be raised with the force than without the force? Answer in degrees.

Correct answer: 13.42

Explanation / Answer

with the force,

Perpendicular to the incline,

N = m g cos33 - 22 = ( 7 x 9.81 x cos33) - 22 = 35.6 N

f = m g sin33 = 37.4 N (along the incline)

u = f / N = 1.05

now without the force,

N = m g cos(theta)

and f = m g sin(theta)

u = f/ N = tan(theta)

theta = tan^-1(1.05) = 46.4 deg .......Ans

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