Question

An object ofmass looka is accelerated
uniformly from a ta velocity of Sml to 8mls in 6s.Calculate the initial and final momentom of theobject. Aste Also find the magnitude of force exertedon the object.​

Answer 1

$\underline{\rm Correct\:Question : }$

An object of mass 100 kg is accelerated uniformly from 5m/s to 8m/s in 6s. Calulcate inital momentum and final momentum. Also find the magnitude of force exerted on object.

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$\underline{\rm Answer :}$

Given :-

• $\rm m = 100 kg$
• $\rm u = 5 m/s$
• $\rm v = 8 m/s$
• $\rm t = 6 sec$

where

$\longrightarrow$m is mass of object.

$\longrightarrow$u is initial velocity.

$\longrightarrow$v is final velocity.

$\longrightarrow$t is time taken.

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To find -

• Initial momentum $\longrightarrow$ $\rm p_1$
• Final momentum $\longrightarrow$ $\rm p_2$
• Force exerted $\longrightarrow$ $\rm F$

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Formula used -

$\boxed{\rm\red{p = mv}}$

• p is momentum
• m is mass of object.
• v is velocity.

$\boxed{\rm\red{F = ma}}$

• F is force.
• m is mass of object.
• a is acceleration.

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$\underline{\rm Solution - }$

$\underline{\rm\pink{ Calculating \:intital\: momentum (p_1) }}$

• $\rm u = 5 m/s$
• $\rm m = 100 kg$

Substituting the value in formula -

$\rm p_1 = mu$

$\implies$$\rm p_1 = 100 \times 5$

$\implies$$\rm p_1 = 500 kg m/s$

$\boxed{\underline{\rm\red{Initial\: momentum = 500 kg m/s }}}$

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$\underline{\rm\pink{Calculating\: final \:momentum (p_2) }}$

• $\rm u = 8 m/s$
• $\rm m = 100 kg$

Substituting the value in formula -

$\rm p_2 = mv$

$\implies$$\rm p_2 = 100 \times 8$

$\implies$$\rm p_2 = 800 kg m/s$

$\boxed{\underline{\rm\red{Final momentum = 800 kg m/s }}}$

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$\underline{\rm\pink{Calculating \:Force -}}$

For calculating force, first we need to calculate acceleration.

Calculating Acceleration -

• $\rm u = 5 m/s$
• $\rm v = 8 m/s$
• $\rm t = 6 sec$

Substituting the value in 1st equation of motion -

$\rm v = u + at$

$\implies$$\rm 8 = 5 + a \times 6$

$\implies$$\rm 3 = 6a$

$\implies$$\rm a = \frac{6}{3}$

$\implies$$\rm a = 2 m/s^2$

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• $\rm m = 100 kg$
• $\rm a = 2 m/s^2$

Substituting the value in formula -

$\rm F = ma$

$\implies$$\rm F = 100 \times 2$

$\implies$$\rm F = 200 N$

$\boxed{\underline{\rm\red{Force exerted = 200N}}}$

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