Question

1. Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road. The same motorcar can be pushed by three persons to produce an acceleration of 0.2 ms with what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort.)

━━━━━━━━━━━━━━━━━━━━━━━━━━
2. A hammer of mass 500 g, moving at 50 m s. strikes a nail. The nail stops the hammer in a very short time of 0.01 s. What is the force of the nail on the hammer?

━━━━━━━━━━━━━━━━━━━━━━━━━━
3. A motorcar of mass 1200 kg is moving along a straight line with a uniform velocity of 90 km/h. Its velocity is slowed down to 18 km/h in 4 s by an unbalanced external force. Calculate the acceleration and change in momentum. Also calculate the magnitude of the force required.


━━━━━━━━━━━━━━━━━━━━━━━━━━
${\sf{\red{\underbrace{\green{Spams \: will \: be \: deleted. }}}}}$
${\sf{\red{\underbrace{\green{Only \: quality \: answers. }}}}}$

​

Answer 1

Answer 1 -

Given -

• Mass of the motor car (m)= 1200 kg

• 2 person push the motor car , so the acceleration acquired by the car is given by the third person

• Acceleration produced by the car pushed by the third person (a) = 0.2 m/s²

To Find -

• Force exerted by each person to push the cart

Formula -

• Force = Mass × Acceleration

• F = MA

Solution -

Force applied by 3rd person (F) = MA

$\dashrightarrow\sf \: 1200 \times 0.2$

$\dashrightarrow\sf \: 240 N$

All persons push the motorcar with the same muscular effort hence which person apply the force of 240 N .

━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2 -

Given -

• Mass of the hammer (m) = 500 g
• → 500/1000
• → 0.5 kg

• Initial velocity of the hammer (u) = 50 m/s

• Time taken by nail to stop the hammer (t) = 0.01 s

• Final velocity of the hammer (v) = 0

To Find -

• Force of the nail on the hammer = ?

Formula -

• Force = Mass × Acceleration

• f = ma ( now we know that the formula of acceleration is ( v - u ) / t

• f = m (v – u) / t

Solution -

Force of the nail on the hammer (f) = m (v - u) / t

$\dashrightarrow\sf \: 0.5 \times \dfrac{0 - 50} { 0.01}$

$\dashrightarrow\sf \: -2500 N$

━━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 3 -

Given -

• Mass of the motor car (m) = 1200 kg

• Initial velocity of the motor car (u) = 90 km/h
• → 90 × 5/18
• → 25 m/s

• Final velocity of the motor car (v) = 18 km/h
• → 18 × 5/18
• → 5 m/s

• Time taken (t) = 4 s

To Find -

• Acceleration (a) = ?

• Change in momentum (ΔP) = ?

• Magnitude of the force (f) = ?

Formula -

• For Acceleration = v = u + at (1st equation of motion )

• For change in momentum = ΔP = mv - mu

• For Magnitude of the force = f = ma

Solution -

Acceleration

$\dashrightarrow\sf \: v = u + at$

$\dashrightarrow\sf \: 5 = 25 + a \times 4$

$\dashrightarrow\sf \: a = -5 m/s^2$ (retardation)

Change in momentum

$\dashrightarrow\sf \: ΔP = mv − mu$

$\dashrightarrow\sf \: ΔP = 1200 \times 5−1200 \times 25$

$\dashrightarrow\sf \: ΔP = -24000 kg m/s$

Magnitude of the force

$\dashrightarrow\sf \: F = M \times A$

$\dashrightarrow\sf \: F = 1200 \times 5$

$\dashrightarrow\sf \: F = 6000 N$

Answer 2

Ans 1 - 240 N

ans 2 - −2500N

Ans 3 - −5m/s2 , −24000kgm/s , 6000N