The coefficient of kinetic friction between a suitcase and the floor is 0.29. If the suitcase has a mass of 76 kg, how far can it be pushed across the level floor with 710 J of work?

To find the distance the suitcase can be pushed across the level floor with 710 J of work, we need to use the following formula:

Work = Force * Distance

First, we need to find the force.

The work done on an object against friction is given by the formula:

Work = Force * Distance

Where:
- Work is the amount of work done (710 J in this case)
- Force is the force applied to overcome friction
- Distance is the distance over which the force is applied

In this case, the force required to overcome friction is the product of the coefficient of kinetic friction (μk) and the normal force (N). The normal force is the force exerted by a surface perpendicular to the object.

The formula for the force of friction is:

Force of Friction = μk * N

Since the suitcase is being pushed across a level floor, the normal force is equal to the weight of the suitcase, which is given by the formula:

Weight = mass * gravity

Where:
- mass is the mass of the suitcase (76 kg in this case)
- gravity is the acceleration due to gravity (9.8 m/s^2)

So, N = mass * gravity

Substituting the given values:

N = 76 kg * 9.8 m/s^2

Next, we can find the force of friction:

Force of Friction = μk * N

Substituting the given value for the coefficient of kinetic friction (0.29) and the calculated value for N:

Force of Friction = 0.29 * (76 kg * 9.8 m/s^2)

Now, we can find the distance over which the force is applied:

Work = Force * Distance

Rearranging the formula:

Distance = Work / Force

Substituting the given value for work and the calculated value for the force of friction:

Distance = 710 J / (0.29 * (76 kg * 9.8 m/s^2))

Calculate the final result to find the distance the suitcase can be pushed across the level floor.