Question

An object of mass 100 kg is accelerated uniformly form a velocity of 5 ms$^{–1}$ to 8 ms$^{–1}$ in 6s. Calculate initial momentum, final momentum and magnitude of force required on the object.​

Answer 1

Answer:

Given:-

Mass of the object (m) = 100 kg.

Initial velocity (u) = 5 ms$^{–1}$

Final velocity (v) = 8 ms$^{–1}$

To find:-

• Initial momentum
• Final momentum
• Magnitude of force required on the object

Solution:-

Initial momentum ${p_1}$ = mass × initial velocity = mu = 100 kg × 5 ms$^{–1}$

= 500 kgms$^{–1}$

Final momentum ${p_2}$ = Mass × final velocity

= 100 kg × 8 ms$^{–1}$

= 800 kgm s$^{–1}$.

Now, magnitude of force required on the object

We know that,

Force = Change in momentum/Time

= (${p_1}$ – ${p_2}$)/t

$= \frac{(800 - 500) \: kgms {}^{ - 1} }{6 \: s}$

= 50 N.

Answer 2

Correct Question:

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

Given:

• Initial Velocity of object, u = 5 m/s
• Final Velocity of object, v = 8 m/s
• Mass of the object, m = 100 kg
• Time taken by object, t = 6 s

To find:

• Initial momentum, final momentum and magnitude of force required on object?

Solution:

We know that,

★ Momentum = mass × velocity

Therefore,

Initial momentum,

⇏ mu = 100 × 5

⇏ 500 kg m/s

Also Final momentum,

⇏ mv = 100 × 8

⇏ 800 kg m/s

∴ Hence, Initial and final momentum of the object is 500 kg m/s and 800 kg m/s respectively.

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Now, Lets Let's calculate the Force exerted on the object,

⇏ F = (mv - mu)/t

⇏ F = (800 - 500)/6

⇏ F = 300/6

⇏ F = 50 N

∴ Hence, Force exerted on the object is 50 N.