A 50.0-kg block is being pushed up a 15.0° slope by a force of 300 N which is directed 30.0° below the slope. The coefficient of kinetic friction between the block and the slope is 0.200. What is the acceleration of the block? A) 0.164 m/s² B) 0.967 m/s² C) 1.20 m/s² D) 2.20 m/s² E) 0.528 m/s²

Question

Quizplus · Accepted Answer

First, we need to resolve the force of 300 N into its components parallel and perpendicular to the slope. The force parallel to the slope is $300\sin 30^\circ = 150$ N, and the force perpendicular to the slope is $300\cos 30^\circ = 259.81$ N.

Next, we need to find the force of kinetic friction acting on the block, which is $\mu_k N$, where $N$ is the normal force. The normal force is equal to the perpendicular force, which is $259.81$ N.

Therefore, the force of kinetic friction is $\mu_k N=0.200(259.81)=51.96$ N.

Now, we can apply Newton's second law along the direction parallel to the slope:
$$\sum F = ma$$
$$150-51.96=50.0a\sin 15^\circ$$
Solving for $a$, we get:
$$a=0.164	ext{ m/s}^2$$

Therefore, the correct choice is A.

A 500-Kg Block Is Being Pushed Up a 15