Question

An object of mass \(40\) \(kg\) is raised to a height of \(5\) \(m\) above the ground. What is its potential energy? If the object is allowed to fall, find its kinetic energy when it is half-way down.

Answer 1

Given: 

Mass of object, \( m = 40 \, \text{kg} \) 
Height, \( h = 5 \, \text{m} \) 
Acceleration due to gravity, \( g = 10 \, \text{m/s²} \)

Step 1: Potential Energy at the top

Potential Energy, \( PE = m g h \) 
\[ PE = 40 \times 10 \times 5 = 2000 \, \text{J} \]

Step 2: Kinetic Energy at half-way down

When the object is half-way down, height above ground = \( h/2 = 2.5 \, \text{m} \) 
Remaining potential energy = \( PE_{\text{remaining}} = m g (h/2) = 40 \times 10 \times 2.5 = 1000 \, \text{J} \) 
Since total mechanical energy is conserved, 
\[ KE + PE_{\text{remaining}} = PE_{\text{top}} \implies KE = 2000 - 1000 = 1000 \, \text{J} \]

Answer:

Potential energy at the top = 2000 J 
Kinetic energy at half-way down = 1000 J