Physics Study Guide: Work, Energy, and Power

Q23. A 15 kg cannonball is launched straight up with a speed of 25 m/s.

• a. How high up will it go?

• b. How much work was done on the cannonball to get it that high?

Background

Topic: Conservation of Energy, Work-Energy Principle

This question tests your understanding of how kinetic energy is converted to gravitational potential energy and how to calculate the work done to reach a certain height.

Key Terms and Formulas

• Kinetic Energy (KE): $KE = \frac{1}{2}mv^2$

• Gravitational Potential Energy (PE): $PE = mgh$

• Work-Energy Theorem: The work done on an object is equal to its change in kinetic energy.

Step-by-Step Guidance

1. First, calculate the initial kinetic energy of the cannonball using $KE = \frac{1}{2}mv^2$ where $m = 15\ kg$ and $v = 25\ m/s$.

2. At the highest point, all the kinetic energy will have been converted into gravitational potential energy: $PE = mgh$.

3. Set the initial kinetic energy equal to the potential energy at the highest point: $\frac{1}{2}mv^2 = mgh$.

4. Solve for $h$ (height): $h = \frac{v^2}{2g}$, where $g = 9.8\ m/s^2$.

Try solving on your own before revealing the answer!

Q24. A 10 kg block is pushed across a friction-free floor by a horizontal force of 50 N. If the distance between points A and B is 7 meters, how much power is used if it takes 4 seconds to go from A to B?

Background

Topic: Work, Power, and Energy

This question tests your ability to calculate work done by a force and the power required to perform that work over a certain time interval.

Key Terms and Formulas

• Work: $W = Fd$

• Power: $P = \frac{W}{t}$

• Where $F$ is force, $d$ is distance, and $t$ is time.

Step-by-Step Guidance

1. Calculate the work done using $W = Fd$, where $F = 50\ N$ and $d = 7\ m$.

2. Once you have the work, use the formula for power: $P = \frac{W}{t}$, where $t = 4\ s$.

Try solving on your own before revealing the answer!

Q25. A 5.0 kg rock is dropped from a cliff 90 meters high. After falling 20 meters, how much kinetic energy does the rock have?

Background

Topic: Conservation of Energy

This question tests your understanding of how gravitational potential energy is converted into kinetic energy as an object falls.

Key Terms and Formulas

• Potential Energy lost: $\Delta PE = mg\Delta h$

• Kinetic Energy gained: $KE = \Delta PE$ (if air resistance is ignored)

• Where $m$ is mass, $g$ is acceleration due to gravity, and $\Delta h$ is the change in height.

Step-by-Step Guidance

1. Calculate the change in height: $\Delta h = 20\ m$.

2. Calculate the potential energy lost: $\Delta PE = mg\Delta h$, where $m = 5.0\ kg$ and $g = 9.8\ m/s^2$.

3. The kinetic energy gained by the rock after falling 20 meters is equal to the potential energy lost.

Try solving on your own before revealing the answer!

Final Answers

Q23a: $h = 31.89\ m$ (using $h = \frac{v^2}{2g}$)

Q23b: $W = 4687.5\ J$ (work equals the change in kinetic energy)

Q24: $P = 87.5\ W$ (work divided by time)

Q25: $KE = 980\ J$ (potential energy lost equals kinetic energy gained)

Each answer is found by applying the relevant formulas and substituting the given values.