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 the object for 10 sec in the direction of its motion. What is the work done by the force ? What is the final momentum and final kinetic energy of the object
Answers
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)