Question

16. An object of mass 100 kg is accelerated uniformly from a velocity
of 5 m s' to 8 m si 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

Given :

• Mass of an object, m = 100 kg

• Initial velocity, u = 5 m/s

• Final velocity, v = 8 m/s

• Time, t = 6 seconds

To find :

• Initial momentum
• Final momentum
• Force exerted on the object

According to the question,

➞ Initial momentum = Mass × Initial velocity

➞ Initial momentum = 100 kg × 5 m/s

➞ Initial momentum = 500 kg m/s

So,the final momentum is 500 kg m/s.

➞ Final momentum = Mass × Final velocity

➞ Final momentum = 100 kg × 8 m/s

➞ Final momentum = 800 kg m/s

So,the final momentum is 800 kg m/s.

Now,

➞ v = u + at

Where,

• v = Final velocity
• u = Initial velocity
• a = Acceleration
• t = Time

➞ 8 = 5 + a × 6

➞ 8 - 5 = 6a

➞ 3 = 6a

➞ 3 ÷ 6 = a

➞ 0.5 = a

So,the acceleration is 0.5 m/s².

As we know,

➞ Force = Mass × Acceleration

Or,

➞ F = ma

➞ F = 100 × 0.5

➞ F = 50 N

So,the force exerted on the object is 50 Newton.

Answer 2

Answer:

Given:-

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

To Find :-

• Initial Mounmentum
• Final Mounmentum
• Force applied

Solution :-

❶ Initial Mounmentum

$\sf \: initial \: mounmentum \: = mass \times initial \: velocity$

Initial Mounmentum = 100 × 5

Hence, Initial Mounmentum = 500 kg m/s.

❷ Final Mounmentum

$\sf \: final \:mounmentum = mass \times final \: velocity$

Final Mounmentum = 100 × 8

Hence, Final Mounmentum = 800 kg m/s

❸ Force exerted

So, for finding force exerted we will first find Acceleration. by using newton first Equation of motion.

$\huge \fbox {v = u + at}$

➵ 8 = 5 + a × 6

➵ 8 - 5 = a × 6

➵ 3 = 6a

➵ 3/6 = a

➵ a = 0.5 m/s²

Hence, Acceleration of body is 0.5 m/s².

Now,

Let's find force exerted

F = ma

➵ F = 100 × 0.5

➵ F = 50

Therefore :-

Force applied = 50 Newton