A worker pushes a heavy 100-kg) crate that is resting on a thick pile carpet. The coefficients of static and kinetic friction are 0.6 and 0.4, respectively. The worker pushes with a horizontal force of 600 N. Use g = 9.8 m/s². The acceleration of the crate will be A) 9.8 m/s². B) 4.9 m/s². C) 3.5 m/s². D) 2.1 m/s². E) 0 m/s².

Question

Quizplus · Accepted Answer

The force of friction acting on the crate can be found using the formula:
friction = coefficient of friction * normal force
where the normal force is equal to the weight of the crate (since it is on a horizontal surface).
friction = 0.6 * 100 * 9.8 = 588 N
Since the force of the worker's push is greater than the force of friction, the crate will accelerate. The acceleration can be found using the formula:
net force = mass * acceleration
where the net force is the force of the worker's push minus the force of friction.
net force = 600 N - 588 N = 12 N
acceleration = net force / mass = 12 N / 100 kg = 0.12 m/s^2
Finally, since the coefficient of kinetic friction is less than the coefficient of static friction, once the crate starts moving, the force of friction will decrease to 0.4 * 100 * 9.8 = 392 N. Thus, the crate will continue to move with a constant velocity (i.e. no more acceleration). Therefore, the acceleration of the crate is 2.1 m/s^2.

A Worker Pushes a Heavy 100-Kg) Crate That Is Resting