Work Energy and Power examples

📚 Quick Study Guide

• 🏋️‍♀️ Work: Work is done when a force causes a displacement. It is calculated as $W = F \cdot d \cdot cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and displacement.
• ⚡ Energy: Energy is the capacity to do work. Kinetic energy (KE) is the energy of motion, $KE = \frac{1}{2}mv^2$, and potential energy (PE) is stored energy, such as gravitational potential energy $PE = mgh$.
• ⚙️ Power: Power is the rate at which work is done or energy is transferred. It is calculated as $P = \frac{W}{t}$, where $W$ is work done and $t$ is time, or $P = F \cdot v$, where $F$ is force and $v$ is velocity.
• 🔥 Work-Energy Theorem: The work done on an object equals the change in its kinetic energy: $W = \Delta KE = KE_f - KE_i$.
• 💡 Conservation of Energy: In a closed system, the total energy remains constant (energy cannot be created or destroyed, only transformed).

Practice Quiz

1. A force of 50 N is applied to move an object 5 meters horizontally. If the force is applied at an angle of 30 degrees to the horizontal, how much work is done?
   1. 125 J
   2. $216.5 \text{ J}$
   3. 250 J
   4. $173.2 \text{ J}$
2. A 2 kg ball is dropped from a height of 10 meters. What is its kinetic energy just before it hits the ground (assuming no air resistance, and $g = 9.8 m/s^2$)?
   1. 98 J
   2. 196 J
   3. 200 J
   4. 49 J
3. A motor does 1200 J of work in 4 seconds. What is the power output of the motor?
   1. 300 W
   2. 4800 W
   3. 1204 W
   4. 0.0033 W
4. A 1000 kg car accelerates from 10 m/s to 20 m/s. What is the work done on the car?
   1. 50,000 J
   2. 100,000 J
   3. 150,000 J
   4. 200,000 J
5. What is the potential energy of a 5 kg object held at a height of 2 meters above the ground (assuming $g = 9.8 m/s^2$)?
   1. 49 J
   2. 98 J
   3. 10 J
   4. 25 J
6. A machine lifts a 50 kg object to a height of 10 meters in 5 seconds. What is the power developed by the machine? ($g = 9.8 m/s^2$)
   1. 980 W
   2. 4900 W
   3. 250 W
   4. 750 W
7. A spring with a spring constant of $k = 200 \text{ N/m}$ is compressed by 0.2 meters. What is the potential energy stored in the spring?
   1. 4 J
   2. 8 J
   3. 20 J
   4. 40 J