Question

a) An object of 40 kg mass is moving with 5 m/s velocity. Now force is applied
on the object such that its velocity increases to 10 m/s. Calculate the work
done by the force.​

Answer 1

Answer:

★ Work done = 1875J ★

Explanation:

Given:

• Mass of object is 40 kg
• Initial velocity (u) is 5m/s
• Final velocity (v) is 10m/s

To Find:

• Work done by the force

Solution: We know that

★ Work done= Force x Displacement ★

• W = F x S

★ Force = Mass x Acceleration ★

• F = M x a

† We can write a = F/m

→ By the third equation of the motion ←

• v² – u² = 2as

$\small\implies{\sf }$ 10² – 5² = 2as

$\small\implies{\sf }$ 100 – 25 = 2 x F/m x s ( Since, a = F/m )

$\small\implies{\sf }$ 75 = 2 x F/50 x s

$\small\implies{\sf }$ 75 = F/25 x s

$\small\implies{\sf }$ 75 x 25 = F x s

$\small\implies{\sf }$ 1875 = F x s

$\small\implies{\sf }$ W = F x S

Hence, Work done by the force is 1875J

__________________________________

★ Solving through another method ★

Given:

• Mass is 50 kg
• Initial velocity (u) is 5m/s
• Final velocity (v) is 10m/s

To Find:

• Work done by the force

Solution: According to the work energy conservation theorem

★ Work done by the Force= Change in Kinetic Energy ★

• Work done by the Force = 1/2 x m ( v² – u² )

$\small\implies{\sf }$ Work done = 1/2 x 50 x ( 100 – 25 )

$\small\implies{\sf }$ Work done = 25 x 75

$\small\implies{\sf }$ Work done = 1875 J

Hence, Work done by the force is 1875J