A boy picks up a stone of mass 5 g and throws it vertically upwards with an initial velocity of 15 m s$^{-1}$ - Leaving Cert Physics - Question 14 - 2022

The principle of conservation of energy states that energy cannot be created or destroyed; it can only be transformed from one form to another. In a closed system, the total energy remains constant.

The main type of energy that the stone's kinetic energy is being converted into as it travels upwards is potential energy. As the stone rises, its speed decreases, and its kinetic energy decreases, while its height increases, leading to an increase in potential energy.

To calculate the kinetic energy (KE) of the stone:

1. Convert mass from grams to kilograms: $m = 5 ext{ g} = 0.005 ext{ kg}$

2. Use the formula for kinetic energy:
   $KE = \frac{1}{2} mv^2$

   Plugging in the values:
   $KE = \frac{1}{2} \times 0.005 \text{ kg} \times (15 ext{ m/s})^2$
   $KE = 0.5625 ext{ J}$

Using the conservation of energy, the kinetic energy will convert to potential energy at maximum height.

1. Set the kinetic energy equal to potential energy:
   $KE = PE$ $0.5625 = mgh$

2. Substitute values to find height (h):
   $0.5625 = 0.005 \cdot 9.8 \cdot h$

3. Rearranging gives:
   $h = \frac{0.5625}{0.005 \cdot 9.8} \approx 11.5 ext{ m}$

The unit of energy is the Joule (J). One Joule is defined as the amount of energy transferred when a force of one newton is applied over a distance of one meter.