An object of mass 20kg is released from a height of 10m above the ground level. The kinetic energy of the object just before it hits the ground is

Analysis

To solve this problem, we need to apply the Law of Conservation of Energy. This law states that energy cannot be created or destroyed, only transformed from one form to another. In this scenario, the object starts with Potential Energy (PE) at the top and converts it into Kinetic Energy (KE) as it falls.

Concept

• Potential Energy (PE): Energy possessed by an object due to its position. The formula is $PE = mgh$.
• Kinetic Energy (KE): Energy possessed by an object due to its motion.
• Conservation Principle: Just before the object hits the ground, all its initial potential energy has been converted into kinetic energy (ignoring air resistance). • Therefore: $KE_{final} = PE_{initial}$

Step-by-Step Solution

1. Identify the given values: • Mass ($m$) = $20\text{ kg}$ • Height ($h$) = $10\text{ m}$ • Acceleration due to gravity ($g$) = $10\text{ m/s}^2$ (Standard value used in JAMB physics unless otherwise specified).

2. Calculate the initial Potential Energy: • $PE = m \times g \times h$ • $PE = 20\text{ kg} \times 10\text{ m/s}^2 \times 10\text{ m}$ • $PE = 2000\text{ J}$

3. Relate to Kinetic Energy: • Since the object is released from rest, its initial kinetic energy is $0$. As it falls, the potential energy is converted entirely into kinetic energy. • $KE = 2000\text{ J}$

Conclusion

The kinetic energy of the object just before it hits the ground is equal to the potential energy it had at the height of 10m, which is 2000J.

Exam Tip

In JAMB Physics, whenever you see a question about an object falling from a height, don't waste time calculating velocity using equations of motion ($v^2 = u^2 + 2as$). Simply use the $PE = mgh$ formula. It is faster and less prone to calculation errors!