A 25.0 kg block is pulled 4.5 meters up a 20° rough incline by an applied force Fa = 200 N, directed up the ramp. The block starts from rest and has a final speed of 1.5 m/s.

Find the following:

a) The total work done on the block, Wtot =___ J
b) The work done on the block by friction, Wf =___ J
c) The force of friction, fk =___ N
d) The coefficient of friction, μk =____

To find the answers to the given questions, we will use the equations of work, energy, and friction.

a) The total work done on the block (Wtot) can be calculated using the work-energy principle, which states that the work done on an object is equal to the change in its kinetic energy. We can express this as:

Wtot = ΔK

Where ΔK is the change in kinetic energy.

In this case, the block starts from rest, so its initial kinetic energy (K_initial) is zero. The final kinetic energy (K_final) can be calculated using the equation:

K_final = (1/2) * m * v^2

Where m is the mass of the block (25.0 kg) and v is the final speed (1.5 m/s).

Plugging in the values, we have:

K_final = (1/2) * 25.0 kg * (1.5 m/s)^2

Calculate K_final to get the final kinetic energy.

Therefore, Wtot = K_final - K_initial.

b) The work done on the block by friction (Wf) can be found using the equation:

Wf = μk * N * d

Where μk is the coefficient of friction, N is the normal force, and d is the displacement of the block.

c) The force of friction (fk) can be determined using the equation:

fk = μk * N

Where μk is the coefficient of friction and N is the normal force.

d) To find the coefficient of friction (μk), we can use the equation for the force of friction and then manipulate it as follows:

μk = fk / N

Now, let's calculate the answers to these questions step-by-step.