Question

Q7. Find the gravitational potential energy of 2 kg mass kept at a height of 2 m above the ground. Calculate its kinetic energy when it falls to ground.

Answer 1

Answer :

Given -

• Mass = 2 kg
• Height = 2 m

To Find -

• Gravitational potential energy ?
• Kinetic energy ?

Solution -

Potential energy = mgh

• Mass = m = 2 kg
• Acceleration due to gravity = g = 9.8 m/s²
• Height = h = 2 m

⇒ mgh

⇒ 2*9.8*2

⇒ 39.2 J

So, gravitational potential energy of the object is 39.2 J.

Kinetic energy = ½mv²

• Mass = m = 2 kg
• Final velocity = ?

Using Newton's equation of motion :

➜ v² - u² = 2as

➜ v² - 0² = 2*9.8*2

➜ v² = 39.2

➜ v = √39.2

➜ v = 6.26 m/s

Hence, Now Finding the Kinetic energy :

⇒ ½*2*(6.26)²

⇒ 6.26²

⇒ 39.1 J

So, kinetic energy of the object when it falls on the ground is 39.1 J.

Answer 2

Given:

• Mass = 2kg
• Height = 2m

To find:

• Kinetic energy ( K.E )
• Gravitational potential energy

Solution:

Finding Kinetic energy (K.E)

Using

K.E = 1/2 mv²

Where

• m : mass
• v : velocity

Firstly finding velocity using the kinematic equation

v² - u² = 2gs

Where

• v : final velocity
• u : initial velocity
• g : acceleration due to gravity
• s : distance travelled

→ v² - 0² = 2(9.8)(2)

→ v² = 19.6 × 2

→ v = √39.2

→ v = 6.26 m/s

Now, finding Kinetic energy

→ K.E = 1/2 × 2 × 6.26²

→ K.E = 6.26²

→ K.E = 39.1 J

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Now, finding Gravitational potential energy

We know that

Potential energy = mgh

Where

• m : mass = 2kg
• g : acceleration due to gravity = 9.8 m/s²
• h : height = 2m

Substituting the values we have

♦ P.E = 2 × 9.8 × 2

♦ P.E = 39.2 J

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Hence , potential energy (P.E) = 39.2 J & Kinetic energy = 39.1 J