A box of books weighing 323 N is shoved across the floor by a force of 477 N exerted downward at an angle of 35° below the horizontal.

(a) If μk between the box and the floor is 0.51, how long does it take to move the box 4.80 m starting from rest?
(b) What is the maximum coefficient of kinetic friction between the box and the floor that allows the box to move from this applied force.

Anyone know how to do this

To find the answers to both parts of the question, we will use the following equations:

1) The force of friction (Ffriction) can be calculated using the equation Ffriction = μk * Normal force, where μk is the coefficient of kinetic friction and Normal force is the force perpendicular to the surface.

2) The acceleration (a) of the box can be calculated using Newton's second law, Fnet = m * a, where Fnet is the net force acting on the box and m is the mass of the box.

3) The time (t) it takes to move the box can be calculated using the equation s = ut + (1/2) * a * t^2, where s is the displacement, u is the initial velocity (which is 0 as the box is at rest), a is the acceleration, and t is the time.

Now let's solve each part of the question.

(a) Calculating the time taken to move the box 4.80 m starting from rest:

First, we need to find the net force acting on the box. The net force is the applied force in the horizontal direction minus the force of friction.
Fapplied = 477 N (given)
Ffriction = μk * Normal force

To find the normal force, we need to resolve the weight of the box into its components. The vertical component of the weight (mg) is canceled out by the normal force.
Downward force = Weight of the box = 323 N
Vertical component of weight = 323 N * cos(35°)
Normal force = upward component of weight = 323 N * cos(35°)
(multiplying by cos(35°) because it's the angle below the horizontal)

Now we can calculate the force of friction:
Ffriction = μk * Normal force

Next, we can find the net force:
Fnet = Fapplied - Ffriction

Using Newton's second law, Fnet = m * a, we can find the acceleration, a.

Finally, we can use the formula s = ut + (1/2) * a * t^2 to find the time, t.

(b) Calculating the maximum coefficient of kinetic friction:

To find the maximum coefficient of kinetic friction, we need to determine the coefficient of kinetic friction that allows the box to move with the given applied force of 477 N.

Again, we can start by finding the net force:
Fnet = 477 N - Ffriction

Using Newton's second law, Fnet = m * a, we can find the acceleration, a.

Then, we can calculate the maximum coefficient of kinetic friction using the equation Ffriction = μk * Normal force.
Since we know Ffriction and Normal force, we can rearrange this equation to solve for μk.

Now that we've explained the approach, we can use the given values and the equations explained above to find the specific answers.