A 55-kg block, starting from rest, is pushed a distance of 5.0 m across a floor by a horizontal force Fp whose magnitude is 140 N. Fp is parallel to the displacement of the block. The final speed of the block is 2.35 m/s.

A) What work did the friction do on the box?
B) What is the coefficient of friction?

Not sure. I need help too*-)

A) The frictional force, opposing the motion, does negative work on the box. To find the work done by friction, we can use the equation: Work = force x displacement x cos(theta), where theta is the angle between the force and displacement vectors. Since the force and displacement are parallel, the angle theta would be 0 degrees.

In this case, the frictional force = Force applied - Force accelerating the block
= Fp - ma (where m is the mass and a is the acceleration)

The acceleration can be found using the equation: Final velocity^2 = Initial velocity^2 + 2a x displacement.
Rearranging this equation, we get: a = (Final velocity^2 - Initial velocity^2) / (2 x displacement)

Given that the initial velocity is 0 m/s and the final velocity is 2.35 m/s, and the displacement is 5.0 m, we can find the acceleration:

a = (2.35^2 - 0^2) / (2 x 5.0) = 2.35^2 / 10 = 0.54725 m/s^2

Now we can calculate the frictional force:

Frictional force = Force applied - (mass x acceleration)
= 140 N - (55 kg x 0.54725 m/s^2)
= 140 N - 30.100375 N
= 109.899625 N

Finally, to find the work done by friction, we can multiply the frictional force by the displacement and cos(theta):

Work = Frictional force x displacement x cos(theta)
= 109.899625 N x 5.0 m x cos(0)
= 109.899625 N x 5.0 m x 1
= 549.498125 J

So, the work done by friction on the box is 549.498125 Joules.

B) To find the coefficient of friction, we can use the equation: Frictional force = coefficient of friction x normal force.
Since there is no information provided about the normal force, we cannot directly calculate the coefficient of friction. However, we can use the equation Fp - (mass x acceleration) = coefficient of friction x normal force.

Using the values we have already calculated, we can substitute them into the equation:

140 N - (55 kg x 0.54725 m/s^2) = coefficient of friction x normal force

Simplifying this equation, we get:

140 N - 30.100375 N = coefficient of friction x normal force

109.899625 N = coefficient of friction x normal force

Therefore, we need information about the normal force, or any other relevant information to calculate the coefficient of friction accurately.

To answer these questions, we need to understand the concept of work and the relationship between work and friction.

A) To find the work done by friction, we need to calculate the work done by all forces on the block and subtract the work done by the applied force.

The work done by a force (W) is given by the equation:

W = F*d*cos(theta)

Where F is the magnitude of the force, d is the displacement, and theta is the angle between the force and the displacement.

In this case, the applied force (Fp) is parallel to the displacement, so the angle theta is 0 degrees.

The work done by the applied force is:

Wp = Fp * d * cos(0) = Fp * d

Wp = 140 N * 5.0 m = 700 J

The total work done on the block is equal to the change in kinetic energy, which is given by:

Wtotal = ΔK

Here, the block starts from rest, so the initial kinetic energy (K₀) is zero. The final kinetic energy (K₁) is given by:

K₁ = (1/2) * m * v²

Where m is the mass of the block and v is the final speed.

K₁ = (1/2) * 55 kg * (2.35 m/s)² = 149.49 J

Therefore, the total work done on the block (Wtotal) is:

Wtotal = K₁ - K₀ = K₁ - 0 = K₁ = 149.49 J

To find the work done by friction (Wf), we subtract the work done by the applied force from the total work:

Wf = Wtotal - Wp = 149.49 J - 700 J = -550.51 J

The negative sign indicates that the work done by friction is in the opposite direction of the displacement, which means it acts to oppose the motion of the block.

Therefore, the work done by friction on the block is -550.51 J.

B) To find the coefficient of friction (μ), we can use the formula:

Wf = μ * N * d

Where Wf is the work done by friction, N is the normal force, and d is the displacement.

The normal force (N) is equal to the weight of the block (mg), which is given by:

N = mg = 55 kg * 9.8 m/s² = 539 N

Using the value of Wf from part A (-550.51 J) and substituting the known values, we get:

-550.51 J = μ * 539 N * 5.0 m

Solving for μ, we find:

μ = -550.51 J / (539 N * 5.0 m)

μ ≈ -0.204

The negative sign indicates that the friction force opposes the displacement, and the coefficient of friction is approximately 0.204.

That is just the previous problem worked backwards with different numbers.