Question

a block of mass 5kg is placed at aheight of 200m, if it allow to fall towards ground . then find the potential energy and kinetic energy of the block after covering 50m​

Answer 1

Given:-

• Mass of body = 5 kg
• Initial height = 200 m

To find:-

• Potential energy (PE) and kinetic energy (KE) after covering 50 m

Answer:-

Finding PE :-

▪As it is given that, total height is 200 m, and we have to find the potential energy after covering 50 m.

▪So, height of the block above the ground = 200 m - 50 m = 150 m

‣ PE = mgh

→ PE = 5 × 10 × 150 J

→ PE = 7500 J Ans.

Finding KE:-

▪For finding KE, we have to find v²

▪Applying third equation of motion from the point the block is dropped till the point it covers 50 m,

v² = u² + 2as

Sign convention: Acceleration and displacement will be negative since it is in downward direction. Putting available values,

→ v² = 0² + [2 × (-10) × (-50)]

→ v² = 1000 (m/s)² ----( 1 )

‣ Now, we know that KE = (1/2)mv²

From ( 1 ),

→ KE = [(1/2) × 5 × 1000]

→ KE = 2500 J Ans.

OR:-

For finding KE:-

☛ We know that total mechanical energy remains conserved during free fall.

❥ Initial Kinetic Energy + Initial Potential Energy = Final Kinetic Energy + Final Potential Energy

⦾ Initial Kinetic energy = 0 J (as the body was allowed to "fall" or its initial velocity was 0 m/s)

⦾ Initial potential energy at the instant the block is released = mgh = 5 × 10 × 200 = 10000 J

⦾ We have already found that, Final potential energy after covering 50 m = 7500 N

Putting this in conversation of mechanical energy equation given above,

→ 0 + 1000 = final KE + 7500

→ final KE (after covering 50 m) = 2500 J Ans.