Question

9) A stone is dropped down a well. When it hits the bottom of the well, it is travelling at 20 m s-1. The mass of the stone is 20 g.
a. Calculate the kinetic energy of the stone as it hits the bottom of the well.
b. What is the gravitational potential energy of the stone at the top of the well?
c. Calculate the height of the well.

Answer 1

Given:-

• Velocity ,v = 20m/s

• Mass ,m = 20/1000kg = 0.02 Kg

• Acceleration due to gravity ,g = 10m/s²

To Find:-

(a.) Calculate the kinetic energy of the stone as it hits the

bottom of the well.

(b.) What is the gravitational potential energy of the stone at the top of the well?

(c.) Calculate the height of the well.

Solution:-

[a]

• KE = 1/2mv2

Where,

KE is the Kinetic Energy

m is the mass

v is the speed/velocity

Substitute the value we get

→ KE = 1/2×0.02 ×20²

→ KE = 1/2 ×0.02 ×400

→ KE = 0.02 × 200

→ KE = 4 J

Therefore, kinetic energy of the stone is 4 Joule.

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[b]

According to Work Energy Theorem .

Gravitational potential energy of the stone at the top of the well is 4 Joule .

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[c]

We have to calculate the height of the well .

• PE = mgh

where,

PE is Potential Energy

m is the mass

g is the acceleration due to gravity

h is the height

Substitute the value we get

→ 4 = 0.02 × 10 × h

→ 4 = 0.2 × h

→ h = 4/0.2

→ h = 20

Therefore, the height of the well is 20 metres.

Answer 2

$\huge \bf \: Given$

Velocity (V) = 20 m/s

Mass (M) = 20 g

Acceleration (A) = 10 m/s²

$\huge \bf \: To \: find$

a. Calculate the kinetic energy of the stone as it hits the bottom of the well.

b. What is the gravitational potential energy of the stone at the top of the well?

c. Calculate the height of the well.

$\huge \bf \: Solution$

$\huge \bf \: 1$

$\huge \bf \: \frac{1}{2} \times {mv}^{2}$

$\sf \: \dfrac{1}{2} \times 0.02 \times (20) {}^{2}$

$\sf 1 \times 0.02 \times 10 \times 20$

$\huge \tt \: \: KE= 4 \: joule$

$\huge \bf \: 2$

According to work energy theorem the gravitional potential energy is 4 joule

$\huge \bf \: 3$

PE = MGH

$\sf \: 4 = 0.02 \times 10 \times h$

$\sf \: 4 = 0.2 \: h$

$\sf \: h \: = \dfrac{4}{0.2}$

$\huge \sf h =20 \: m$