What is the potential energy of a 25 kg bicycle resting at the top of a hill 3 m high? (Formula: $P E=m g h$)
The problem requires calculating the gravitational potential energy of a bicycle with a mass of \(m = 25 \text{ kg}\) positioned at a height of \(h = 3 \text{ m}\). The formula for gravitational potential energy is given as \(PE = mgh\), where \(g\) is the acceleration due to gravity, approximately \(9.8 \text{ m/s}^2\). We need to determine the potential energy in Joules (J).
To find the potential energy, we substitute the given values into the formula:
\[PE = m \times g \times h\]
\[PE = 25 \text{ kg} \times 9.8 \text{ m/s}^2 \times 3 \text{ m}\]
First, we multiply the mass and the height: \(25 \times 3 = 75\).
Then, we multiply this result by the gravitational constant \(9.8\):
\[PE = 75 \times 9.8 = 735 \text{ J}\]
Thus, the potential energy of the bicycle is \(735 \text{ J}\).
Potential energy is a fundamental concept in physics used to understand how much energy an object stores due to its position in a gravitational field. For example, when you climb a staircase, your body does work against gravity, increasing your potential energy, which is later released as kinetic energy when you walk down. Similarly, engineers use this principle when designing roller coasters, where a car is lifted to a high point to store potential energy that will propel it through the track. Calculating this energy helps in predicting the motion and safety of objects in various mechanical systems.