Question

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

Answer 1

ANSWER :

mass of the object = 100 kg.

time taken = 6 sec.

initial velocity = 5 m/s.

final velocity = 8 m/s.

initial momentum of the object = 100*5=500 kg.m/s.

final momentum of the object =  100*8=800 kg.m/s.

force required = rate of change of momentum / time taken.

force=(800 - 500) / 6

force=300/6

force= 50 N.

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Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

★Given :-

m = 100 kg

u = 5 m/s

v = 8 m/s

t = 6 s

★Hence now :-

${\boxed{\sf\:{Initial\;momentum = mu}}}$

= 100 × 5

= 500 kg m/s

${\boxed{\sf\:{Final\;momentum = mv}}}$

= 100 × 8

= 800 kg m/s

★Using formula :-

$\tt{\rightarrow Force=\dfrac{Change\;in\; Momentum}{Time}}$

$\tt{\rightarrow Force=\dfrac{800 - 500}{6}}$

$\tt{\rightarrow Force=\dfrac{300}{6}}$

Force = 50 Newton

$\boxed{\begin{minipage}{11 cm} Additional Information \\ \\ \ Final\;Velocity=Initial\; velocity+Acceleration\times Time \\ \\ Momentum = Mass\times Velocity \\ \\ Force=Mass\times Acceleration \\ \\ Force = \dfrac{Change\;in\;Momentum}{Time\;Interval} \\ \\ Impulse = Force\times Time \end{minipage}}$