7. Imagine that the coefficient of kinetic friction between a certain 15-kg box and the floor is 0.35. How hard would you have to push on it to move it at a constant speed of 2.6 m/s across the floor?

The force will not depend upon speed, as long as the speed is constant.

The required force is
M*g*(mu_k) newtons

mu_k is the kinetic friction coefficient.

To determine how hard you would have to push on the box to move it at a constant speed, we need to use the concept of friction and Newton's laws of motion.

First, let's calculate the force of friction acting on the box. The force of friction can be found using the formula:

frictional force = coefficient of kinetic friction * normal force

Given that the coefficient of kinetic friction is 0.35, we need to determine the normal force. The normal force is the force exerted by the floor on the box perpendicular to the surface. In this case, the normal force is equal to the weight of the box, which can be calculated using the formula:

weight = mass * gravity

where the mass of the box is 15 kg and the acceleration due to gravity is approximately 9.8 m/s^2.

weight = 15 kg * 9.8 m/s^2 = 147 N

Next, we can calculate the force of friction:

frictional force = 0.35 * 147 N = 51.45 N

To move the box at a constant speed of 2.6 m/s, we need to apply a force equal to the force of friction, but in the opposite direction. This is because the force we apply needs to overcome the force of friction. Therefore, the force required to push the box can be calculated as:

pushing force = force of friction = 51.45 N

Therefore, to move the box at a constant speed of 2.6 m/s across the floor, you would have to push it with a force of approximately 51.45 N.