Alex works at a legal firm which produces a lot of documents. Often Alex has to carry heavy stacks of documents from one office to another. On this particular day Alex, who weighs 75 kilograms, has to transport a stack of documents which weighs10 kilograms. He has to lift them 5 meters from the floor and then carry them to an office 100 meters down the hall, where he will drop them on the floor. Alex walks swiftly at a steady rate of 1 meter per second. What two pieces of information given in the above description will help you compute the amount of work Alex does when he lifts the papers? After Alex has lifted the papers, he pauses a moment to rest. What type of energy do the papers he is holding possess? When Alex finishes carrying the papers, he drops them on the floor. What type of energy do the papers possess as the drop? Is the energy of the stack of papers when Alex holds them equal to the energy of the papers dropping on the floor? Why or why not?
To compute the amount of work Alex does when lifting the papers, we need two pieces of information given in the description:
1. Alex's weight: Alex weighs 75 kilograms.
2. The height he lifts the papers: Alex lifts the papers 5 meters from the floor.
To compute the work done, we can use the formula:
Work = Force x Distance x cos(θ)
In this case, the force exerted by Alex is equal to his weight, which is 75 kg multiplied by the acceleration due to gravity (9.8 m/s^2) which equals 735 N (Newtons). The distance Alex lifts the papers is given as 5 meters.
Plug in these values into the formula:
Work = 735 N x 5 m x cos(θ)
Since the angle θ is not mentioned, we assume it to be vertical, which means cos(θ) is 1. Therefore, the work done by Alex when he lifts the papers is:
Work = 735 N x 5 m = 3675 Joules (J)
After Alex has lifted the papers, they possess gravitational potential energy. Gravitational potential energy is the energy associated with an object's height relative to a reference point, in this case, the floor. So, the papers Alex is holding possess gravitational potential energy.
When Alex drops the papers on the floor, they possess kinetic energy. Kinetic energy is the energy associated with the motion of an object. As the papers fall, their potential energy is converted into kinetic energy.
The energy of the stack of papers when Alex holds them (gravitational potential energy) is not equal to the energy of the papers dropping on the floor (kinetic energy). This is because energy is conserved throughout the process, but it is converted from one form to another. When the papers are lifted, work is done to change their position against gravity, increasing their potential energy. When they drop, the potential energy is converted into kinetic energy. Thus, the two energies are different forms of energy, but their total energy remains the same, neglecting any other energy losses (such as air resistance).