Question

An object with 100 N weight is raised to a height of 15 m find the potential energy possessed by the object at that height. Also find the new potential energy :
A. If the same object is raised half of its original height
B. If the same object is raised to three times of its original height ​

Answer 1

It is given that, weight of the object is 100 N.

We know,

$PE \ or \ E_p = mgh = Wh$

(∵ W = mg)

Energy at 15 m from ground:-

PE = $(100N)(15 m)$

⇒ PE $1500 \ Nm$

⇒ PE = $1500 J$ or $1.5 \ kJ$

Energy at half of it's original height:-

Height = ½(15 m) = 7.5 m

∴ PE = $(100N)(7.5m)$

⇒ PE = $750 J$ or $0.75 kJ$

Energy at tripled original height:-

Height = 15 m × 3 = 45 m

∴ PE = $(100 N)(45 m)$

⇒ PE = $4500 J$ or $4.5 kJ$.

Answer 2

$\bold{Answer\;:-}$

Given :-

• Mass of the object, m = 100 N

• Height to which it is raised, h = 15 m

Formulas :-

• PE = mgh.

• F = mg

• W = mgh = F × h

Solution :-

• PE = mgh

• PE = 100 N × 15 m

• PE = 1500 J or 1.500 kJ :-

A. Height to which it is raised now = 15/2 = 7.5 m

• PE = 100 N × 7.5 m

• PE = 750 J or 0.750 kJ

B. Height to which it is raised now = 15 × 3 = 45 m

• PE = 100 N × 45 m

• PE = 4500 J or 4.500 kJ

Extra : Derivation of potential energy.

• Work done = Force × Displacement

• Force = Mass × Acceleration or Mass × Acceleration due to gravity

• Work done = Mass × Acceleration due to gravity × Displacement

• Displacement = Height

• Work done = Mass × Acceleration due to gravity × Height

• Potential energy = Work done

• Potential energy = Mass of the body × Acceleration due to gravity × Height to which the bidy is raised.

$\bold{Hope\;it \; helps\;!}$