Question

16. An object of mass 100 kg is accelerated uniformly from a velocity
of 5 m s–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.

Answer 1

Answer:

Explanation:

Initial velocity of the object, u = 5 m/s

Final velocity of the object, v = 8 m/s

Mass of the object, m = 100 kg

Time take by the object to accelerate, t = 6 s

Initial momentum = mu = 100 — 5 = 500 kg m sˆ’1

Final momentum = mv = 100 — 8 = 800 kg m sˆ’1

Force exerted on the object, F = mv – mu / t

= m (v-u) / t

= 800 – 500

= 300 / 6

= 50 N

Initial momentum of the object is 500 kg m sˆ’1.

Final momentum of the object is 800 kg m sˆ’1.

Force exerted on the object is 50 N.

Answer 2

$\boxed{\rm{\blue{Find \longrightarrow }}}$

• The initial and final momentum of the object
• Magnitude of the force exerted on the object.

$\boxed{\rm{\orange{Given \longrightarrow }}}$

• Initial velocity [u] = 5 m/s
• Final velocity [v] = 8 m/s
• Mass [ m ]= 100 kg
• Time take by the object to accelerate, t = 6 s

$\boxed{\rm{\red{SoLution \longrightarrow }}}$

Initial momentum = $\sf{mu = 100 - 5 = 500 kg m/s}$

Final momentum = $\sf{mv = 100 - 8 = 800 kg m/s}$

Force exerted on the object, $\boxed{\sf{F = \dfrac{mv - mu}{ t}}}$

$\sf{F= \dfrac{m (v-u) }{t}}$

$\sf{F=\dfrac{100(8-5)}{6}}$

$\sf{ F= \dfrac{800-500}{6} }$

$\sf{ F= \dfrac{300}{6} }$

$\bf {F= 50 N}$

$\bf{\underline{\therefore Initial\ momentum\ of\ the\ object\ is\ 500 kg m/s}}$

$\bold {\bf{\underline{\therefore Final\ momentum\ of\ the\ object\ is\ 800 kg m/s}}}$

$\bold {\bf {\underline { force = 50 N}}}$

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