A) An 8.00 kg mass is at rest on an incline, the angle of the incline is 32.0°.

Question

A) An 8.00 kg mass is at rest on an incline, the angle of the incline is 32.0°. The incline has a rough surface (Ms = 0.375 and Mk = 0.250). A force F is applied to the mass in the horizontal direction, toward the direction up the incline. Find the force F where the motion of the object up the incline is imminent.

B) Add 2.00 N to your value for F found in part a). Calculate how fast the object is moving after a displacement of 15.0 m up the incline, and how long it would take for the object to travel this distance.

Explanation / Answer

normal force = mg * cos(theta) + F * sin(theta)

static friction = Ms * normal force

to just start motion

mg * sin(theta) = F * cos(theta) + Ms * (mg * cos(theta) + F * sin(theta))

8 * 9.8 * sin(32) = F * cos(32) + 0.375 * (8 * 9.8 * cos(32) + F * sin(32))

A) F = 15.87 N

after adding 2 N force

mg * sin(theta) - F * cos(theta) - Ms * (mg * cos(theta) + F * sin(theta)) = ma

8 * 9.8 * sin(32) - 17.87 * cos(32) - 0.375 * (8 * 9.8 * cos(32) + 17.87 * sin(32)) = 8 * a

a = 0.261 m/s^2

by second equation of motion

s = ut + 0.5 * at^2

15 = 0 + 0.5 * 0.261 * t^2

t = 10.72 sec

time taken = 10.72 sec

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