Question

An object of mass 100 kg is accelerated uniformly from a velocity of 5 m 5-1 to 8 m s-1 in 6 s. Calculate the
initial and final momentum of the object. Also find the magnitude of the force exerted on the object.
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Answer 1

Given:

• Mass,m = 100 kg

• initial velocity, u = 5 m/s

• Final velocity, v = 8 m/s

• Time taken, t = 6 s

To be calculated:

Calculate the initial and final momentum of the object. Also find the magnitude of the force exerted on the object ?

Solution:

★ Initial momentum = mass × initial velocity

= 100 × 5

= 500 kg.m/s ........( i )

★ Final Momentum = mass × final velocity

= 100 × 8

= 800 kg.m/s........( ii )

Now,

Force = Change in momentum/Time taken

= 800 - 500 / 6 [ From ( i ) & ( ii ) ]

= 300 / 6

= 50 N

Thus,magnitude of the force exerted on the object is 50 N.

Answer 2

Explanation :

Mass of object is 100 kg. Accelerating uniformly from 5 m/s to 8 m/s in 6 seconds.

What is initial momentum? What is final momentum? What is force exerted by object?

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At first we will find initial momentum.

We know,

Initial momentum (p) = m × u

⇒ Initial momentum = 100 × 5

⇒ Initial momentum = 500

⇒ Initial momentum = 500 kg m/s

∴ Initial momentum = 500 kg m/s (1)

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Now we know that,

Final momentum (p') = m × v

⇒ Final momentum = 100 × 8

⇒ Final momentum = 800

⇒ Final momentum = 800 kg m/s

∴ Final momentum = 800 kg m/s (2)

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Now we have to find acceleration of object at first.

Acceleration (a) = (v - u)/t

⇒ Acceleration = (8 - 5)/6

⇒ Acceleration = 3/6

⇒ Acceleration = 0.5 m/s²

Now we know that,

Force exerted (F) = m × a

⇒ Force = 100 × 0.5

⇒ Force = 50

⇒ Force = 50 N

∴ Force exerted by object = 50 N (3)

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