Question

A 100.-newton box is pulled up a 20.-meter-long incline by a constant force of 80. newtons. The vertical height gained by the box is 10. meters. 2) Explain why there is a difference between the total work done by the 80.-newton force in pulling the box to the top of the incline and the amount of gravitational potential energy gained by the box as it was pulled to the top of the incline. Correct Answer: — The work is converted into forms of energy other than gravitational potential energy (e.g. thermal or kinetic energy). — Friction causes internal energy to increase, so not all the work done becomes gravitational potential energy. 3) Determine the total amount of gravitational potential energy, in joules, gained by the box as it is pulled to the top of the incline. Correct Answer: — 1.0 x 103 J or 1000 J

Answer 1

The difference between the total work done by the force and the amount of gravitational potential energy gained by the box is due to the conversion of work into other forms of energy. The total amount of gravitational potential energy gained by the box can be calculated using the formula PE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height. In this case, the gravitational potential energy gained by the box is
`1.0 * 10^3` Joules.

The difference between the total work done by the 80-newton force in pulling the box to the top of the incline and the amount of gravitational potential energy gained by the box is due to the conversion of the work into other forms of energy. When the box is pulled up the incline, some of the work is converted into thermal energy or kinetic energy. Additionally, friction causes an increase in internal energy, so not all the work done becomes gravitational potential energy.

The total amount of gravitational potential energy gained by the box as it is pulled to the top of the incline can be calculated using the formula:

Gravitational potential energy (PE) = mass (m) × acceleration due to gravity (g) × height (h)

Given that the mass of the box is 100 kg, the acceleration due to gravity is 9.8 m/s², and the height gained by the box is 10 meters, we can calculate the gravitational potential energy as follows:

`PE = 100 kg * 9.8 m/s^2 * 10 m = 1.0 * 10^3 Joules`