Question

16. An object of mass 100 kg is accelerated uniformly from a velocity
of 5 ms-1 to 8 ms- 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

• Mass of the object, m = 100 kg

• Initial velocity, u = 5 m/s

• Final velocity, v = 8 m/s

• Time, t = 6 s

• Let a be the acceleration.

• Let p be the momentum.

• Let the force be f.

Momentum, p = mv

Initial momentum, p = mu

$p = 100 \times 5 \\ \\ p = 500 \: kg \frac{m}{s}$

Initial momentum of the object is 500 kgm/s.

Final momentum, p = mv

$p = 100 \times 8 \\ \\ p = 800 \: kg \frac{m}{s}$

Final momentum of the object is 800 kgm/s.

According to first equation of motion,

v = u + at

$8 = 5 +( a \times 6) \\ \\ 8 - 5 = 6a \\ \\ 3 = 6a \\ \\ a = \frac{3}{6} \\ \\ a = \frac{1}{2} \\ \\ a = 0.5 \: \dfrac{m}{ {s}^{2} }$

The acceleration of the object is 0.5 m/s².

According to the result of Newton's second law of motion, f = ma.

$f = 100 \times 0.5 \\ \\ f = 100 \times \frac{1}{2} \\ \\ f = 50 \: newton$

The magnitude of force exerted on the object is 50 N.

Answer 2

Answer:

Given :-

• An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms to 8 m/s in 6 seconds.

To Find :-

• What is the initial and final momentum.
• What is the magnitude of the force exerted on the object.

Formula Used :-

❶ To find initial momentum we know that,

★ Initial momentum = Mass × Initial velocity ★

❷ To find final momentum we know that,

✪ Final momentum = Mass × Final velocity ✪

❸ To find force exerted on the object we know that,

❖ Force = (mv - mu) / t ❖

Solution :-

Given :

• Initial velocity = 5 m/s
• Final velocity = 8 m/s
• Mass = 100 kg
• Time = 6 seconds

❶ To find initial momentum,

↦ Initial momentum = 100 kg × 5 m/s

➦ Initial momentum = 500 kg m/s

$\rule{150}{1}$

❷ To find final momentum,

⇒ Final momentum = 100 kg × 8 m/s

➠ Final momentum = 800 kg m/s

$\rule{150}{1}$

❸ To find force exerted on the object,

↪ Force = (800 - 500) / 6

↪ Force = (300) / 6

↪ Force = 300 / 6

➲ Force = 50 N

$\rule{150}{1}$

Therefore,

• Initial momentum = 500 kg m/s
• Final momentum = 800 kg m/s
• Force exerted on the object = 50 N