Question

19. An object of mass 5 kg is moving with an initial momentum of 20 kg m /s. A force of 2.0 N acts on an object for

10 s in the direction of the motion. What is the work done by the force? What is the final momentum and final

kinetic energy of the object?​

Answer 1

Answer:

Mass of object = 5kg

Initial momentum = 20 kg m/s

Magnitude of applied force = 2N

Time interval = 10s

We have to find

Word done by the force

Final momentum

Final kinetic energy

★ As per newton's second law of motion, force is measured as the rate of change of linear momentum of moving object.

Mathematically, F = ∆p/∆t

F denotes force

∆p denotes change in momentum

∆t denotes time

⧪ Final momentum :

➠ F = p₂ - p₁/∆t

➠ 2 = p₂ - 20/10

➠ p₂ = 20 + 20

➠ p₂ = 40 kg m/s ___ (I)

⧪ Final kinetic energy :

Relation between kinetic energy and momentum is given by, k = p²/2m

where m denotes mass of body

➠ k₂ = p₂²/2m

➠ k₂ = (40)²/2(5)

➠ k₂ = 1600/10

➠ k₂ = 160 J ___ (II)

⧪ Work done by force :

As per work - kinetic energy theorem, w = ∆k

w denotes work done

∆k denotes change in kinetic energy

So first we need to find initial kinetic energy of object

➠ k₁ = p₁²/2m

➠ k₁ = (20)²/2(5)

➠ k₁ = 400/10

➠ k₁ = 40 J

Let's calculate work done by force!

→ W = ∆k = k₂ - k₁

→ W = 160 - 40

→ W = 120 J ___ (III)

Explanation: