The coefficient of kinetic friction between a suitcase and the floor is 0.26. If the suitcase has a mass of 70.0 {kg}, how far can it be pushed across the level floor with 680 {J} of work?

To find the distance the suitcase can be pushed across the level floor with a given amount of work, we need to use the work-energy principle.

The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the suitcase can be calculated using the equation:

Work = force * distance

Since the suitcase is being pushed along the floor, the force applied is the product of the coefficient of kinetic friction and the normal force. The normal force is equal to the weight of the suitcase, given by:

Weight = mass * gravity

where the mass is 70.0 kg and gravity is approximately 9.8 m/s^2.

So the force of friction can be calculated as:

Force of friction = coefficient of kinetic friction * normal force

Once we know the force of friction, we can calculate the distance using the formula:

Work = force of friction * distance

Therefore, the steps to find the distance the suitcase can be pushed are as follows:

1. Calculate the normal force using the equation: Weight = mass * gravity.
2. Calculate the force of friction using the equation: Force of friction = coefficient of kinetic friction * normal force.
3. Rearrange the equation to solve for distance: distance = work / force of friction.
4. Substitute the given values into the equation to find the distance.

Let's go through these steps step-by-step using the given values:

1. Calculate the normal force:
Weight = 70.0 kg * 9.8 m/s^2
= 686 N

2. Calculate the force of friction:
Force of friction = 0.26 * 686 N
= 178.36 N

3. Calculate the distance:
distance = 680 J / 178.36 N
≈ 3.81 m

Therefore, the suitcase can be pushed approximately 3.81 meters across the level floor with 680 J of work.