Question

Helpppp please...

a person pushes a box across a horizontal floor with an initial velocity of 5.2 m/s. the box has a mass of 22 kg, and the coefficient of kinetic friction between the box and the floor is 0.44. how far does the box slide before coming to rest?

Answer 1

To find the distance the box slides before coming to rest, calculate the acceleration of the box using the equations of motion and consider the effects of friction.

Step-by-step explanation:

To find the distance the box slides before coming to rest, you need to use the equations of motion and consider the effects of friction. First, calculate the acceleration of the box using the equation:

net force = mass * acceleration

Since the frictional force is the only force acting on the box, use:

frictional force = coefficient of kinetic friction * normal force

Then, use the equation:

acceleration = change in velocity / time

Assuming the box starts from rest, the initial velocity is 0, and you can rearrange the equation to:

change in velocity = acceleration * time

Finally, use the equation:

distance = (initial velocity * time) + (1/2 * acceleration * time^2)

Answer 2

The box slides approximately 2.3 meters before coming to rest.

Step-by-step explanation:

To find how far the box slides before coming to rest, we can use the equation for the force of friction:

friction force = coefficient of kinetic friction × normal force

First, let's calculate the normal force:

The weight of the box is given by weight = mass × gravitational acceleration. The gravitational acceleration is approximately 9.8 m/s². So, the weight of the box is 22 kg × 9.8 m/s².

The normal force is equal to the weight because the box is on a horizontal floor. Therefore, the normal force is also equal to 22 kg × 9.8 m/s².

Now, we can substitute the values into the equation for the friction force:

friction force = 0.44 × (22 kg × 9.8 m/s²)

Finally, we can calculate the distance the box slides before coming to rest using the equation:

friction force = mass × acceleration

We can rearrange the equation to solve for the distance:

distance = initial velocity² / (2 × acceleration)

Substituting in the initial velocity and acceleration, we find:

distance = (5.2 m/s)² / (2 × (0.44 × (22 kg × 9.8 m/s²)))

Calculating this, we find that the box slides approximately 2.3 meters before coming to rest.