## large truck and a car,

[question] Question. A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision. If the collision lasts for 1 s (a)Which vehicle experiences greater force of impact ? (b)Which vehicle experiences greater change in momentum ? (c)Which vehicle experiences greater acceleration ? (d)Why is the car likely to suffer more damage than the truck ? [solution] Solution: Let mass of truck $=\mathrm{M} ;$ mass of car $=\mathrm{m} ;$ velocity of truck $=\mathrm{v} ;$ time fo...

## A motorcar of mass 1200 kg is moving along a straight line

[question] Question. 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 to18 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. [/question] [solution] Solution: (i) Initial velocity of the car, $\mathrm{u}=90 \mathrm{~km} / \mathrm{h}=25 \mathrm{~ms}^{-1}$; final velocity of the car, $\mathrm{v}=18 \mathrm{~km} / \mathrm{h}=$ $5 ...

## A hammer of mass 500 g, moving at 50 ms–1,

[question] Question. A hammer of mass 500 g, moving at 50 ms–1, 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 ? [/question] [solution] Solution: The force of nail on the hammer $F=\frac{\text { Change in momentum of hammer }}{\text { Time }}$ $\mathrm{F}=\frac{\mathrm{m}(\mathrm{v}-\mathrm{u})}{\mathrm{t}}=\frac{0.5(0-50)}{0.01}=-2500 \mathrm{~N}$ Negative sign denotes that the force of nail on the hammer is acting in the di...

## Two persons manage to push a motorcar of mass 1200 kg at a uniform velocity along a level road.

[question] Question. 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–2. With what force does each person push the motorcar ? (Assume that all persons push the motorcar with the same muscular effort.) [question] [solution] Solution: As two persons can make the motorcar move with uniform velocity, it is clear that total force applied by them on the motorcar is balan...

## The following is the distance-time table of an object in motion

[question] Question. The following is the distance-time table of an object in motion (a) What conclusion can you draw about the acceleration ? Is it constant, increasing, decreasing or zero ? (b) What do you infer about the force acting on the object? [/question] [solution] Solution: (a) A careful observation of the distance-time table shows that $\mathrm{s} \propto \mathrm{t}^{3}$. It is known that, in uniform motion $\mathrm{s} \propto \mathrm{t}$, and for motion with uniform acceleration $\ma...

## How much momentum will a dumb-bell of mass 10 kg

[question] Question. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm and does not rebound ? Take its downward acceleration to be 10 ms–2. [question] [solution] Solution: Mass of dumb-bell, $m=10 \mathrm{~kg} ;$ initial velocity, $u=0 ;$ final velocity, $v=? ;$ distance, $\mathrm{s}=80 \mathrm{~cm}=0.8 \mathrm{~m} ;$ acceleration, $\mathrm{a}=10 \mathrm{~ms}^{-2}$ We know $\mathrm{v}^{2}-\mathrm{u}^{2}=2 \mathrm{as}$ $\mathrm{v}^{2}-(0)^{2...

## Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity .

[question] Question. Akhtar, Kiran and Rahul were riding in a motorcar that was moving with a high velocity on an expressway when an insect hit the windshield and got stuck on the windscreen. Akhtar and Kiran started pondering over the situation. Kiran suggested that the insect suffered a greater change in momentum as compared to the change in momentum of the motorcar (because the change in the velocity of the insect was much more than that of the motorcar). Akhtar said that since the motorcar w...

## An object of mass 100 kg is accelerated uniformly from a velocity

[question] Question. An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms–1 to 8 ms–1 in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object. [/question] [solution] Solution: Mass of object, $\mathrm{m}=100 \mathrm{~kg}$; initial velocity, $\mathrm{u}=5 \mathrm{~ms}^{-1} ;$ final velocity, $\mathrm{v}=8 \mathrm{~ms}^{-1} ;$ time, $\mathrm{t}=6 \mathrm{~s}$ Initial momentum $=\mathrm{mu}=100 \times 5=500 \ma...

## An object of mass 1 kg travelling in a straight line with a velocity of 10 ms–1 collides with,

[question] Question. An object of mass 1 kg travelling in a straight line with a velocity of 10 ms–1 collides with, and sticks to a stationary wooden block of mass 5 kg. Then they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object. [/question] [solution] Solution: For object : $\mathrm{m}_{1}=1 \mathrm{~kg} ; \mathrm{u}_{1}=10 \mathrm{~ms}^{-1}$ For wooden block: $\ma...

## A bullet of mass 10 g travelling horizontally with a velocity

[question] Question. A bullet of mass 10 g travelling horizontally with a velocity of 150 ms–1 strikes a stationary wooden block and comes to rest in 0.03 s. Calculate the distance of penetration of the bullet into the block. Also calculate the magnitude of the force exerted by the wooden block on the bullet. [/question] [solution] Solution: Mass of bullet, $\mathrm{m}=10 \mathrm{~g}=0.01 \mathrm{~kg} ;$ initial velocity of bullet, $\mathrm{u}=150 mathrm{~ms}^{-1} ;$ final velocity of bullet, $\...

## A hockey ball of mass 200 g travelling at 10 ms–1 is struck

[question] Question. A hockey ball of mass 200 g travelling at 10 ms–1 is struck by a hockey stick so as to return it along its original path with a velocity of 5 ms–1. Calculate the change of momentum which occurred in the motion of the hockey ball by the force applied by the hockey stick. [/question] [solution] Solution: Mass of ball, $\mathrm{m}=200 \mathrm{~g}=0.2 \mathrm{~kg} ;$ initial velocity of ball, $\mathrm{u}_{1}=10 \mathrm{~ms}^{-1} ;$ final velocity of ball, $\mathrm{u}_{2}=-5 \mat...

## According to the third law of motion when we push on an object,

[question] Question. According to the third law of motion when we push on an object, the object pushes back on us with an equal and opposite force. If the object is a massive truck parked along the roadside, it will probably not move. A student justifies this by answering that the two opposite and equal forces cancel each other. Comment on this logic and explain why the truck does not move. [question] [solution] Solution: When we push a massive truck parked along the roadside, it does not move. ...

## Two objects, each of mass 1.5 kg,

[question] Question. Two objects, each of mass 1.5 kg, are moving in the same straight line but in opposite directions. The velocity of each object is 2.5 ms–1 before the collision during which they stick together. What will be the velocity of the combined object after collision ? [/question] [solution] Solution: Let the objects be $\mathrm{A}$ and $\mathrm{B}$ moving from opposite directions in the same straight line. $\therefore$ Initial momentum of $\mathrm{A}=\mathrm{m} \times \mathrm{v}$ $=...

## Using a horizontal force of 200 N,

[question] Question. Using a horizontal force of 200 N, we intend to move a wooden cabinet across a floor at a constant velocity. What is the friction force that will be exerted on the cabinet ? [question] [solution] Solution: In order to move the cabinet with constant velocity, the net force acting on it should be zero, such that the forces are balanced. This is possible only if the frictional force is 200 N and acts in the direction opposite to the direction of motion of the cabinet....

## From a rifle of mass 4 kg,

[question] Question. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with a speed of 35 ms–1 Calculate the recoil speed of the rifle [question] [solution] Solution: Mass of rifle $=4 \mathrm{~kg}$ Let velocity of recoil of rifle $=\mathrm{v}$ Momentum of the rifle $=4 \times \mathrm{v}$ Mass of bullet $=50 \mathrm{~g}=\frac{50}{1000} \mathrm{~kg}=0.05 \mathrm{~kg}$ Velocity of bullet $=35 \mathrm{~ms}^{-1}$ Momentum of bullet $=0.05 \times 35$ Using the law of conservation of momentum,...

## Explain, why is it difficult for a fireman to hold a hose pipe

[question] Question. Explain, why is it difficult for a fireman to hold a hose pipe which ejects large amounts of water at high velocity. [/question] [solution] Solution: We can explain the above observation on the basis of law of conservation of momentum. When the system of hose and water is not ejecting any water, its momentum is zero. When the water issues out from the hose with a high velocity, it has momentum in the forward direction. Therefore, in order to conserve momentum, the hose tends...

## If action is always equal to the reaction,

[question] Question. If action is always equal to the reaction, explain how a horse can pull a cart. [/question] [solution] Solution: When a horse pulls a cart with a certain force, then the cart pulls the horse with the same force and the system of horse and cart should not move. But, if we analyse the problem carefully, then horse not only applies force on the cart, but also pushes the earth backward with his feet. The earth reacts back to this action of the horse and pushes it in the forward ...

## Why do you fall in the forward direction when a moving bus applies brakes

[question] Question. Why do you fall in the forward direction when a moving bus applies brakes to stop and fall backward when it accelerates from rest ? [/question] [solution] Solution: When a moving bus applies brakes, our feet come to rest with the bus. But upper part of our body continues to move forward on account of inertia of motion. That is why we tend to fall in the forward direction. However, when the bus accelerates from rest, lower part of our body moves with the bus. The upper part o...

## Explain why some of the leaves may get detached

[question] Question. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch. [question] [solution] Solution: When we shake a branch of a tree vigorously, some of the leaves may get detached on account of inertia of rest of the leaves. The branch comes in motion and the leaves try to be in the position of rest. Therefore, they get detached. [solution]...

## In the following example, .

[question] Question. In the following example, try to identify the number of times the velocity of the ball changes. "A football player kicks a football to another player of his team who kicks the football towards the goal. The goalkeeper of the opposite team collects the football and kicks it towards a player of his own team". Also identify the agent supplying the force in each case. [question] [solution] Solution: The velocity of the football changes four times First time the velocity changes ...

## Which of the following has more inertia :

[question] Question. Which of the following has more inertia : (a) a rubber ball and a stone of the same size ? (b) a bicycle and a train ? (c) a five rupees coin and a one-rupee coin ? [/question] [solution] Solution: Mass of a body is the measure of its inertia i.e., more the mass, more is the inertia. Keeping this in mind : (a) Stone has more inertia. (b) Train has more inertia. (c) Five rupees coin has more inertia. [/solution]...