Question

1. what is the potential energy of a 300 kilogram wrecking ball suspended above a hole that is 50 meters deep?
2. how much work is done when a person applies 10 n to a crate to move it 8 meters?
3. a person does 125 joules of work in order to move a couch 5 meters. what amount of force did the person have to use to move the couch?
4. what is the kinetic energy of a 20 kg bike and rider moving at a velocity of 3 m/s?
5. what is the kinetic energy of a 250 kilogram cart rolling at a velocity of 5 m/s?
6. a jet fighter weighs approximately 100,000 kg. if it is traveling at a height of 10,000 meters, what would the potential energy be?
7. what type of energy transfer is occurring when a battery goes from being unused to being in use/turned on?

a. electrical → mechanical
b. chemical → electrical
c. mechanical → electrical
d. electrical → chemical

1. what type of energy transfer is occurring when a person eats food?

a. nuclear → chemical
b. chemical → mechanical
c. mechanical → chemical

Explanation:

Step1: Identify the formula for potential energy

The formula for gravitational potential energy is \(PE = mgh\), where \(m\) is the mass (\(m = 300\space kg\)), \(g\) is the acceleration due to gravity (\(g= 9.8\space m/s^{2}\)), and \(h\) is the height (\(h = 50\space m\)).

Step2: Substitute the values into the formula

$$
LATEXBLOCK0
$$

Step3: Identify the formula for work

The formula for work is \(W = Fd\), where \(F\) is the force (\(F = 10\space N\)) and \(d\) is the distance (\(d=8\space m\)).

Step4: Substitute the values into the formula for work

$$
LATEXBLOCK1
$$

Step5: Rearrange the work formula to find force

From \(W = Fd\), we can solve for \(F\) as \(F=\frac{W}{d}\). Given \(W = 125\space J\) and \(d = 5\space m\).

Step6: Substitute the values to find force

$$
LATEXBLOCK2
$$

Step7: Identify the formula for kinetic energy

The formula for kinetic energy is \(KE=\frac{1}{2}mv^{2}\), where \(m\) is the mass (\(m = 20\space kg\)) and \(v\) is the velocity (\(v = 3\space m/s\)).

Step8: Substitute the values into the kinetic - energy formula

$$
LATEXBLOCK3
$$

Step9: Use the kinetic - energy formula for another case

For \(m = 250\space kg\) and \(v = 5\space m/s\), \(KE=\frac{1}{2}mv^{2}\).

Step10: Substitute the values

$$
LATEXBLOCK4
$$

Step11: Calculate potential energy for the jet fighter

Using \(PE = mgh\), with \(m = 100000\space kg\), \(g = 9.8\space m/s^{2}\), and \(h = 10000\space m\)

$$
LATEXBLOCK5
$$

Step12: Analyze energy transfer in a battery

A battery stores chemical energy. When in use, it converts chemical energy to electrical energy. So for question 9, the answer is B. Chemical → Electrical.

Step13: Analyze energy transfer when a person eats food

Food has chemical energy. When a person eats food, the body converts the chemical energy in food into mechanical energy (for movement etc.). So for question 10, the answer is B. Chemical → Mechanical.

Answer:

1. \(147000\space J\)
2. \(80\space J\)
3. \(25\space N\)
4. \(90\space J\)
5. \(3125\space J\)
6. \(9.8\times 10^{9}\space J\)
7. B. Chemical → Electrical
8. B. Chemical → Mechanical