A 4.8‒kg block on a 39° inclined plane is acted on by a horizontal force of 46 N as shown below. The coefficient of kinetic friction between the block and the plane is 0.33. (a) What is the acceleration of the block if it is moving up the plane? (b) With the horizontal force still acting, how far up the plane will the block go if it has an initial speed of 4.3 m/s? (c) What happens to the block after it reaches the highest point? Give an argument to back your answer.

(a) To find the acceleration of the block moving up the inclined plane, we need to consider the forces acting on the block.

The weight of the block can be separated into two components: the force acting parallel to the inclined plane (mg*sinθ) and the force acting perpendicular to the plane (mg*cosθ). Here, m is the mass of the block and θ is the angle of the inclined plane.

The force of kinetic friction acting on the block can be calculated using the coefficient of kinetic friction (μ) and the force perpendicular to the plane (mg*cosθ). So, the force of kinetic friction (fk) is given by fk = μ * (mg * cosθ).

The net force acting on the block in the direction up the plane is equal to the horizontal force (46 N) minus the force of kinetic friction (fk). So, the net force (Fnet) is Fnet = 46 N - fk.

Using Newton's second law, Fnet = ma, where m is the mass of the block and a is the acceleration.

Substituting the values and solving the equation, we can find the acceleration of the block.

(b) To determine how far up the plane the block will go with an initial speed, we can use the equation of motion:

v^2 = u^2 + 2as

Here,
v = final velocity (which is 0 m/s at the highest point),
u = initial velocity (4.3 m/s),
a = acceleration (which can be taken as the value obtained in part (a)),
s = displacement (which is the distance up the plane we need to find).

By substituting the known values and solving the equation, we can determine the distance the block will travel up the plane.

(c) Once the block reaches the highest point, it will start moving down the inclined plane due to the gravitational force pulling it in that direction. This happens because the horizontal force applied (46 N) is not sufficient to overcome the force of gravity and the force of kinetic friction acting on the block.

At the highest point, the vertical component of the weight (mg*cosθ) acting downwards will be greater than the horizontal force applied (46 N). Therefore, the block will start moving back down the inclined plane under the influence of gravity and the force of kinetic friction.

In summary, after reaching the highest point, the block will start moving back down the inclined plane due to the gravitational force and the force of kinetic friction.