Question

A child does 350 J of work while pulling a box from the ground up to his tree house at a steady speed with a light rope. The tree house is 4.0 m above the ground. What is the mass of the box?

Answer 1

To find the mass of the box, you can 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 box is 350 J and the box is being pulled at a steady speed, so its kinetic energy remains constant.

Step-by-step explanation:

To find the mass of the box, we can 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 box is 350 J and the box is being pulled at a steady speed, so its kinetic energy remains constant. Therefore, the work done is equal to zero.

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

Work = Force x Distance x cos(theta)

Since the work done is zero, we can rearrange the formula to find the force:

Force = -Work / (Distance x cos(theta))

Given that the distance is 4.0 m and the force is the weight of the box, we can calculate the mass of the box using the formula:

Weight = mass x gravity

where gravity is the acceleration due to gravity. Rearranging the formula gives:

mass = weight / gravity

Answer 2

To calculate the mass of the box, we can use the concept of work and gravitational potential energy. By applying the formula mgh = work done, where m is the mass of the box, g is the acceleration due to gravity, and h is the height the box is lifted, we can solve for the mass. In this case, the mass of the box is approximately 9 kg.

Step-by-step explanation:

To calculate the mass of the box, we need to apply the concept of work and gravitational potential energy. The work done on an object can be calculated by multiplying the force applied by the distance over which the force is applied. In this case, the work done is 350 J. The work done is equal to the change in gravitational potential energy of the box, which can be calculated using the formula mgh, where m is the mass of the box, g is the acceleration due to gravity (approximately 9.8 m/s²), and h is the height the box is lifted (4.0 m). So, we have mgh = 350 J.

Substituting the values into the equation, we get (m)(9.8 m/s²)(4.0 m) = 350 J.
Simplifying the expression, we find that the mass of the box is approximately 9 kg.