Question

an object of mass 240 kilogram is accelerated uniformly from a velocity of 4 metre per second to 12 meter per second in 6 seconds. calculate the:. (i) initial momentum (ii) final momentum (iii) magnitude of the force acting on the object​

Answer 1

Given :

▪ Mass of object = 240kg

▪ Initial velocity = 4mps

▪ Final velocity = 12mps

▪ Time interval = 6s

To Find :

✒ Initial momentum (Pi)

✒ Final momentum (Pf)

✒ Force acts on object (F)

Concept :

➡ This question is completely based on concept of Newton's second law of motion.

➡ As per this law, force is defined as the rate of change in momentum. (wrt time)

Mathematically,

$\bigstar\:\underline{\boxed{\bf{\purple{F=\dfrac{\Delta P}{\Delta t}}}}}$

• F denotes force
• ΔP denotes change in momentum
• Δt denotes time interval

Calculation :

⚾ Initial momentum :

→ Pi = mu

→ Pi = 240×4

→ Pi = 960 kgm/s

⚾ Final momentum :

→ Pf = mv

→ Pf = 240×12

→ Pf = 2880 kgm/s

⚾ Force acts on body :

→ F = ΔP/Δt

→ F = (Pf - Pi)/Δt

→ F = (2880-960)/6

→ F = 1920/6

→ F = 320N

Answer 2

Given :-

Mass of Object, m = 240 kg

Intitial velocity, u = 4 m/s

final velocity, v = 12 m/s

time taken , t = 6 sec

To find :-

(I) Initial momentum

(II) Final momentum

(III) Magnitude of Force on object

Solution :-

Using Formula

$\boxed{ \bf{momentum = mass \times velocity}}$

Initial momentum = m u =( 240 × 4 ) kg m/s

❖ Initial momentum = 960 kg m/s.

And

Final momentum = m v = ( 240 × 12 ) kg m/s

❖ Final momentum = 2880 kg m/s.

Now,

Using

$\boxed{ \bf{acceleration = \frac{final \: velocity - initial \: velocity}{time \: taken} }}$

so,

Acceleration = ( v - u) / t

Acceleration = ( 12 - 4 ) / 6

Acceleration = 8 /6 m/s²

As we know

Force = mass × acceleration

so,

Force = 240 × 8 / 6 N

❖ Force = 320 N.