How Do You Calculate Potential Energy and Work in Physics Problems?

[nemzy]

i am confused on how to solve these problems..thanks

You drop a 1.80 kg textbook to a friend who stands on the ground 10.0 m below the textbook with outstretched hands 1.50 m above the ground

(d) If the gravitational potential energy of that system is zero at ground level, what is its potential energy U when the textbook reaches the hands?

(e) How much work Wg is done on the textbook by its weight as it drops to your friend's hands if U is 100 J at the ground level.

(f) What is the change U in the gravitational potential energy of the textbook-Earth system during the drop if U is 100 J at the ground level.


(h) Find U at the hands when U is 100 J at the ground level.

 

[HallsofIvy]

"(d) If the gravitational potential energy of that system is zero at ground level, what is its potential energy U when the textbook reaches the hands?"

Surely you know that the difference in potential energy is "mgh" where m is the mass, g is the acceleration due to gravity (9.81 m/s² in MKS) and h is the height. (Be sure to calculate the distance between the original height of the book and the height of the person's hands.)

"(e) How much work Wg is done on the textbook by its weight as it drops to your friend's hands if U is 100 J at the ground level."

Work done by gravity is the change in potential energy. Caution: since only the change is important whether U= 0 or 100J at ground level is irrelevant!

"(f) What is the change U in the gravitational potential energy of the textbook-Earth system during the drop if U is 100 J at the ground level. "

Someone is having a little fun with you! The answers to these three problems are all exactly the same! They are all really asking for change in U (and the 100 J is still irrelevant).

"(h) Find U at the hands when U is 100 J at the ground level."

Finally a problem where that "100 J" is important. Again, change in U is mgh. Here, of course, h is the 1.50 height of the hands above the ground. Multiplying mgh will give you the change in U from the ground to the hands. Adding the "base" 100J to that gives the actual potential energy, U, at the hands.

 

[M98Ranger]

Potential energy is a concept that can be confusing, but with practice and understanding of the formulas involved, you can solve these problems. Let's break down each question and go through the steps to solve them.

(d) To find the potential energy of the textbook when it reaches your friend's hands, we can use the formula U = mgh, where m is the mass of the textbook (1.80 kg), g is the acceleration due to gravity (9.8 m/s²), and h is the height difference between the textbook and your friend's hands (10.0 m - 1.50 m = 8.50 m). Plugging in these values, we get U = (1.80 kg)(9.8 m/s²)(8.50 m) = 154.44 J. So the potential energy of the textbook when it reaches your friend's hands is 154.44 J.

(e) Work is defined as the force applied over a distance, so we can use the formula W = Fd to find the work done by the weight of the textbook. The weight of the textbook is its mass multiplied by the acceleration due to gravity, so we have F = mg. Substituting this into the work formula, we get W = (mg)d. Plugging in the values given in the problem, we get W = (1.80 kg)(9.8 m/s²)(10.0 m - 1.50 m) = 139.86 J. Therefore, the work done by the weight of the textbook is 139.86 J.

(f) The change in potential energy is simply the final potential energy minus the initial potential energy. In this case, the final potential energy is 154.44 J (from part d) and the initial potential energy is 100 J (given in the problem). So the change in potential energy is 154.44 J - 100 J = 54.44 J.

(h) To find the potential energy at the hands when U is 100 J at the ground level, we can use the same formula as in part d. However, we need to find the height difference between the textbook and your friend's hands. Since the textbook is dropped from a height of 10.0 m and your friend's hands are 1.50 m above the ground, the height difference is 10.0 m - 1.50 m = 8.50