A 2.92 kg block starts from rest at the top of a 30° incline and accelerates uniformly down the incline, moving 1.93 m in 1.60 s.

(a) Find the magnitude of the acceleration of the block. __ m/s2

(b) Find the coefficient of kinetic friction between the block and the incline. ___

(c) Find the magnitude of the frictional force acting on the block.___ N

(d) Find the speed of the block after it has slid a distance 1.93 m. __ m/s

a) x = 1/2 at^2

solve for a
c) mg sin30 - Ff = ma
solve for Ff
b) Fn = mg cos30
mu = Ff/Fn
d) v^2 = 2ax

To solve this problem, we can use the principles of Newton's laws of motion. Let's break down each part of the question and explain how to solve it.

(a) Find the magnitude of the acceleration of the block.

The acceleration of the block can be determined using the equation:

acceleration = (change in velocity) / (time)

In this case, we know that the block starts from rest, so the initial velocity is 0 m/s. The block moves a distance of 1.93 m in 1.60 s.

acceleration = (1.93 m) / (1.60 s)

Calculating this gives us the magnitude of the acceleration of the block.

(b) Find the coefficient of kinetic friction between the block and the incline.

To find the coefficient of kinetic friction, we need to determine the net force acting on the block. The block is subjected to two forces: the component due to gravity (mg*sin(30°)) acting down the incline, and the force of friction acting up the incline.

The net force can be calculated using the equation:

net force = mass * acceleration

Since the block moves uniformly, the net force is zero. Therefore, the force of friction must be equal to the component of gravity acting down the incline.

force of friction = mg*sin(30°)

The coefficient of kinetic friction can be determined using the equation:

coefficient of kinetic friction = force of friction / (mass * g)

Substituting the known values, we can calculate the coefficient of kinetic friction.

(c) Find the magnitude of the frictional force acting on the block.

The magnitude of the frictional force acting on the block is equal to the force of friction we calculated in the previous step.

(d) Find the speed of the block after it has slid a distance of 1.93 m.

To find the speed of the block, we can use the equation:

velocity = initial velocity + (acceleration * time)

Since the block starts from rest, the initial velocity is 0 m/s. We already know the acceleration from part (a), and the time is given as 1.60 s. Plugging in these values will give us the speed of the block after it has slid a distance of 1.93 m.

By following these steps, you can find the answers to the given questions.