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

Solution :-

$\boxed{\bf Potential \ energy = mgh}$

• m = Mass
• g = Acceleration due to gravity
• h = Height

Here :-

• m = 40 kg
• g = 10 m/s²
• h = 5 m

$\longrightarrow \sf P.E = 40 \times 10 \times 5 \\\\\longrightarrow \bf P.E = 2000J$

Potential energy = 2000J

When object is allowed to fall half way down :-

Height = 5/2 = 2.5 m

Initial velocity, u = 0 m/s

We can find final velocity (v) using third equation of kinematics.

$\boxed{\bf v^2 - u^2 = 2gh}$

$\longrightarrow \sf v^2 - 0^2 = 2\times 10 \times 2.5 \\\\\longrightarrow v^2= 50 \\\\\longrightarrow \bf v= \sqrt{50} \ m/s$

$\boxed{\bf Kinetic \ energy = \dfrac{1}{2} mv^2}$

$\longrightarrow \sf K.E = \dfrac{1}{2} \times 40 \times (\sqrt{50} )^2 \\\\\longrightarrow K.E = \dfrac{1}{2} \times 40\times 50 \\\\\longrightarrow K.E = \dfrac{1}{2} \times 2000 \\\\\longrightarrow\bf K.E = 1000J$

Kinetic energy of the object when it is allowed to fall half way down = 1000J