Work-Energy Theorem examples in real life

📚 Quick Study Guide

🔍 The Work-Energy Theorem states that the net work done on an object is equal to the change in its kinetic energy. 💡 Formula: $W_{net} = \Delta KE = KE_f - KE_i = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$, where $W_{net}$ is the net work, $KE$ is kinetic energy, $m$ is mass, $v_f$ is final velocity, and $v_i$ is initial velocity. 🍎 Work is done when a force causes a displacement. $W = Fd\cos(\theta)$, where $F$ is the force, $d$ is the displacement, and $\theta$ is the angle between the force and displacement vectors. ⚡ Positive work increases kinetic energy, while negative work decreases it. 🎢 Examples include: a car accelerating, a ball being thrown, and a roller coaster moving up and down.

Practice Quiz

1. A car accelerates from rest to 20 m/s. Which statement best describes the work-energy theorem in this scenario?
   1. The work done by the engine equals the car's final potential energy.
   2. The work done by the engine equals the car's final kinetic energy.
   3. The work done by the engine equals the car's initial kinetic energy.
   4. The work done by the engine is zero.
2. A baseball with a mass of 0.15 kg is thrown with a speed of 40 m/s. What is its kinetic energy?
   1. 30 J
   2. 60 J
   3. 120 J
   4. 240 J
3. A box is pushed across a floor with a force of 10 N over a distance of 5 meters. If the work done is 50 J, what is the angle between the force and the displacement?
   1. 0 degrees
   2. 45 degrees
   3. 90 degrees
   4. 180 degrees
4. A roller coaster car is moving at 5 m/s at the top of a hill. As it rolls down, its speed increases to 15 m/s. What happened to the kinetic energy?
   1. It decreased.
   2. It remained constant.
   3. It increased.
   4. It became zero.
5. A hockey puck slows down due to friction on the ice. According to the work-energy theorem, what kind of work is done by friction?
   1. Positive work
   2. Negative work
   3. Zero work
   4. Constant work
6. A crane lifts a 100 kg object 10 meters vertically. What is the work done by the crane? (Assume $g = 9.8 m/s^2$)
   1. 98 J
   2. 980 J
   3. 9800 J
   4. 98000 J
7. A spring with a spring constant $k$ is compressed a distance $x$. What is the work done on the spring?
   1. $kx$
   2. $\frac{1}{2}kx$
   3. $kx^2$
   4. $\frac{1}{2}kx^2$