Question

An object of mass 35 kg is accelerated uniformly from a velocity of 5m/s to 8m/s in 10 sec. Calculate the initial and final momentum of the object and find the force exerted on the object.

Answer 1

Given :

▪ Mass of object = 35kg

▪ Initial velocity = 5mps

▪ Final velocity = 8mps

▪ Time interval = 10s

To Find :

▪ Initial and final momentum of object.

▪ Force exerted on the object.

Solution :

→ 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 of object wrt time.

→ Momentum is defined as the product of mass and velocity.

☞ P = mv

☞ F = ΔP/Δt = (Pf - Pi)/Δt

• Pi denotes initial momentum
• Pf denotes final momentum
• Δt denotes interval of time
• ΔP denotes change in momentum
• F denotes force exerted on body

____________________________

✴ Initial momentum :

→ Pi = m × u

→ Pi = 35 × 5

→ Pi = 175 kg*m/s

✴ Final momentum :

→ Pf = m × v

→ Pf = 35 × 8

→ Pf = 280 kg*m/s

✴ Force exerted on body :

✒ F = (Pf - Pi)/Δt

✒ F = (280-175)/10

✒ F = 105/10

✒ F = 10.5N

____________________________

• Force and momentum both are vector quantities.
• Vector quantity has both magnitude as well as direction.

Answer 2

$\rule{200}5$

$\huge\tt{GIVEN:}$

• An object of mass 35 kg is accelerated uniformly from a velocity of 5m/s to 8m/s in 10 sec.

$\rule{200}2$

$\huge\tt{TO~FIND:}$

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

$\rule{200}2$

$\huge\tt{CONCEPT~USED:}$

Newton's Second Law of Motion : Force is defined as the rate of charge in the momentum of an object wrt time. Momentum is defined as the product of mass and Velocity.

P = mv

F = ∆P / ∆T = (Pf - Pi) /∆t

where,Pi = momentum, Pf = final momentum, ∆t = interval of time , ∆p = change in momentum , F = force exerted on a body

$\rule{200}2$

$\huge\tt{SOLUTION:}$

INITIAL MOMENTUM :

↪Pi = m × u

↪Pi = 35 × 5

↪Pi = 175 Kg×m/sec

$\rule{200}2$

FINAL MOMENTUM :

↪Pf = m × v

↪Pf = 35 × 8

↪Pf = 280 Kg×m/sec

$\rule{200}2$

FORCE EXERTED ON THE BODY :

↪F = (Pf - Pi) / ∆t

↪F = (280-175)/10

↪F = 105/10

↪F = 10.5N

$\rule{200}5$