FORCE AND LAWS OF MOTION

What is momentum? Write its SI unit. Interpret force in terms of momentum.
Represent the following graphically
(a) momentum versus velocity when mass is fixed.
(b) momentum versus mass when velocity is constant.

Using second law of motion, derive the relation between force and
acceleration. A bullet of 10 g strikes a sand-bag at a speed of 103 m s-1 and
gets embedded after travelling 5 cm. Calculate
(i) the resistive force exerted by the sand on the bullet
(ii) the time taken by the bullet to come to rest.

Water sprinkler used for grass lawns begins to rotate as soon as the water
is supplied. Explain the principle on which it works.

Two friends on roller-skates are standing 5 m apart facing each other. One
of them throws a ball of 2 kg towards the other, who catches it, How will
this activity affect the position of the two? Explain your answer.

A truck of mas sM is moved under a force F. If the truck is then loaded with
an object equal to the mass of the truck and the driving force is halved,
then how does the acceleration change?

Suppose a ball of mass m is thrown vertically upward with an initial speed v, its
speed decreases continuously till it becomes zero. Thereafter, the ball begins to
fall downward and attains the speed v again before striking the ground. It
implies that the magnitude of initial and final momentums of the ball are same.
Yet, it is not an example of conservation of momentum. Explain why ?

A horse continues to apply a force in order to move a cart with a constant
speed. Explain why?

Two identical bullets are fired one by a light rifle and another by a heavy
rifle with the same force. Which rifle will hurt the shoulder more and why?

Two balls of the same size but of different materials, rubber and iron are
kept on the smooth floor of a moving train. The brakes are applied suddenly
to stop the train. Will the balls start rolling? If so, in which direction? Will
they move with the same speed? Give reasons for your answer.

There are three solids made up of aluminium, steel and wood, of the same
shape and same volume. Which of them would have highest inertia?

There are three solids made up of aluminium, steel and wood, of the same
shape and same volume. Which of them would have highest inertia?

A large truck and a car, both moving with a velocity of magnitude v, have a head-on collision and both of them come to a halt after that. If the collision lasts for 1 s:

(a) Which vehicle experiences the greater force of impact?

(b) Which vehicle experiences the greater change in momentum?

(c) Which vehicle experiences the greater acceleration?

(d)Why is the car likely to suffer more damage than the truck?

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.

A hammer of mass 500 g, moving at 50 m s - '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?

 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 m s-2.With what force does each person push the motorcar? (Assume that all persons push the motorcar with the same muscular effort)

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 forces acting on the object?

How much momentum will a dumbbell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m s-2.

Akhtar, Kiran and Rahul were riding in a motorocar 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 was moving with a larger velocity, it exerted a larger force on the insect. And as a result the insect died. Rahul while putting an entirely new explanation said that both the motorcar and the insect experienced the same force and a change in their momentum. Comment on these suggestions.

 An object of mass 100 kg is accelerated uniformly from a velocity of 5 m s-1 to 8 m s-1in 6 s. Calculate the initial and final momentum of the object. Also, find the magnitude of the force exerted on the object.

An object of mass 1 kg travelling in a straight line with a velocity of 10 m s-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.

A bullet of mass 10 g travelling horizontally with a velocity of 150 m s-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.

A hockey ball of mass 200 g travelling at 10 m s-1is struck by a hockey stick so as to return it along its original path with a velocity at 5 m s-1. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.

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.

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 m s-1 before the collision during which they stick together. What will be the velocity of the combined object after collision?

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?

What is the momentum of an object of mass m, moving with a velocity v?

An automobile vehicle has a mass of 1500 kg. What must be the force between the vehicle and road if the vehicle is to be stopped with a negative acceleration of 1.7 m s-2 ?

A 8000 kg engine pulls a train of 5 wagons, each of 2000 kg, along a horizontal track. If the engine exerts a force of 40000 N and the track offers a friction force of 5000 N, then calculate:

A stone of 1 kg is thrown with a velocity of 20 m s-1 across the frozen surface of a lake and comes to rest after travelling a distance of 50 m. What is the force of friction between the stone and the ice?

A batsman hits a cricket ball which then rolls on a level ground. After covering a short distance, the ball comes to rest. The ball slows to a stop because

(a) the batsman did not hit the ball hard enough.

(b) velocity is proportional to the force exerted on the ball.

(c) there is a force on the ball opposing the motion.

(d) there is no unbalanced force on the ball, so the ball would want to come to rest.

Why is it advised to tie any luggage kept on the roof of a bus with a rope?

When a carpet is beaten with a stick, dust comes out of it. Explain.

An object experiences a net zero external unbalanced force. Is it possible for the object to be travelling with a non-zero velocity? If yes, state the conditions that must be placed on the magnitude and direction of the velocity. If no, provide a reason.

Two objects of masses 100 g and 200 g are moving along the same line and direction with velocities of 2 m s -1 and 1 m s-1 , respectively. They collide and after the collision, the first object moves at a velocity of 1.67 m s -1.Determine the velocity of the second object.

From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m s -1.Calculate the initial recoil velocity of the rifle.

Explain, why is it difficult for a fireman to hold a hose, which ejects large amounts of water at a high velocity.

If action is always equal to the reaction, explain how a horse can pull a cart.

Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.

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.

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?