Question

The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 5 s. Find (a) the momentum before the action of force (b) the momentum after the action of force (c) the magnitude of force.

Answer 1

Answer

Initial momentum = 40 kg.m/s

Final momentum = 80 kg.m/s

Magnitude of force = 8 N

Given

Mass of a body , m = 10 kg

Initial velocity , u = 4 m/s

Final velocity , v = 8 m/s

Time , t = 5 s

To Find

a . Momentum before the action of force

b . Momentum after the action of force

c . Magnitude of force

Formula Applied

Momentum is defined as product of mass and velocity'

$\bigstar\ \; \bf P=mv$

where ,

• P denotes momentum
• m denotes mass
• v denotes velocity

Force is defined as product of mass and acceleration

$\bigstar\ \; \bf F=ma$

where ,

• F denotes force
• m denotes mass
• a denotes acceleration

Solution

a . Momentum before the action of force

velocity before action of force is ,

Initial velocity , u = 4 m/s

mass , m = 10 kg

Initial Momentum , P = ? kg.m/s

So ,

⇒ P = mu

⇒ P = (10)(4)

⇒ P = 40 kg.m/s

________________________

b . Momentum after the action of force

Velocity after action of force is ,

Final velocity , v = 8 m/s

Mass , m = 10 kg

Final Momentum , P = ? kg.m/s

So ,

⇒ P = mv

⇒ P = (10)(8)

⇒ P = 80 kg.m/s

________________________

c . The magnitude of force

Acceleration is defined as rate of change in velocity .

$\implies \rm a=\dfrac{v-u}{t}\\\\\implies \rm a=\dfrac{8-4}{5}\\\\\implies \rm a=\dfrac{4}{5}\ m/s^2$

Now ,

$\rm F=ma\\\\\implies \rm F=(10)\left(\dfrac{4}{5}\right)\\\\\implies \rm F=8\ N$

So , Magnitude of the force = 8 N

________________________

Answer 2

Explanation:

Given that, the velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 5 s.

We have to find (a) the momentum before the action of force (b) the momentum after the action of force (c) the magnitude of force.

Momentum is defined as mass and velocity.

(a) The momentum before the action of force

P = mu

(Where P is momentum, m is mass and u is initial velocity)

→ P = 10 × 4

→ P = 40 kg m/s

(b) The momentum after the action of force

P = mv

(Where P is momentum, m is mass and v is final velocity)

→ P = 10 × 8

→ P = 80 kg m/s

(c) The magnitude of force

Force is defined as product of mass and acceleration.

→ Force = Mass × Acceleration

→ Force = 10 × a ...................................(1)

Using the first equation of motion,

v = u + at

Substitute the known values,

→ 8 = 4 + a(5)

→ 4 = 5a

→ 0.8 = a

Substitute value of a in (1)

→ Force = 10 × 0.8

→ Force = 8N