Physics: Forces and Energy - Kinetic and Potential Energy

A $2\text{ kg}$ book is lifted to a shelf that is $3\text{ m}$ high. Calculate the Gravitational Potential Energy ($E_p$) gained by the book. (Assume $g = 9.8\text{ m/s}^2$)

$E_p = mgh = 2\text{ kg} \times 9.8\text{ m/s}^2 \times 3\text{ m} = 58.8\text{ J}$

The potential energy is found by multiplying the mass, the acceleration due to gravity, and the vertical height.

A toy car with a mass of $0.5\text{ kg}$ is moving at a velocity of $4\text{ m/s}$. Determine its Kinetic Energy ($E_k$).

$E_k = \frac{1}{2}mv^2 = \frac{1}{2} \times 0.5\text{ kg} \times (4\text{ m/s})^2 = 0.25 \times 16 = 4\text{ J}$

To find kinetic energy, square the velocity first, then multiply by the mass and divide by two.

A ball of mass $0.1\text{ kg}$ is dropped from a height of $5\text{ m}$. Ignoring air resistance, what is its velocity ($v$) just before it hits the ground?

$mgh = \frac{1}{2}mv^2 \implies gh = \frac{1}{2}v^2 \implies v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} = \sqrt{98} \approx 9.9\text{ m/s}$

Using the Conservation of Energy, the initial potential energy at the top is converted entirely into kinetic energy at the bottom.