CONCEPT NOTES
Force: It is a push or pull on an object that produces acceleration in the body on which it acts.
S.I. unit of force is Newton.
A force can do three things on a body.
(a) It can change the speed of a body.
(b) It can change the direction of motion of a body.
(c) It can change the shape of a body.
Balanced forces: Forces are said to be balanced forces if they nullify one another and their resultant force is zero.
Unbalanced forces: When two opposite forces acting on a body, move a body in the direction of the greater force or forces which brings motion in a body are called as unbalanced forces.
First law of motion: An object remains in a state of rest or of uniform motion in a straight line unless acted upon by an external unbalanced force.
Inertia: The natural tendency of an object to resist a change in their state of rest or of uniform motion is called inertia.
The mass of an object is a measure of its inertia.
Its S.I. unit is kg.
A body with greater mass has greater inertia.
Frictional force: The force that always opposes the motion of objects is called force of friction.
Second law of motion: The rate of change of momentum of an object is proportional to the applied unbalanced force in the direction of the force. Mathematically.
F=ma
Momentum: The momentum of an object is the product of its mass and velocity and has the same direction as that of the velocity. Its S.I. unit is kg m/s
p=mv
1 Newton: A force of one Newton produces an acceleration of 1 m/s2 on an object of mass 1 kg
Third law of motion: To every action, there is an equal and opposite reaction and they act on two different bodies.
Action = – Reaction
F1 = – F2
Conservation of momentum: If the external force on a system is zero, the momentum of the system remains constant i.e., in an isolated system, the total momentum remains conserved.
NCERT SOLUTIONS (By Concept Academy)
NCERT Textbook Page 118
1. 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?
Ans. (a) A stone of the same size (b) a train (c) a five-rupees coin
As the mass of an object is a measure of its inertia, objects with more mass have more inertia.
2. 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.
Ans.
| Agent supplying the force | Change in velocity of ball |
| 1. First player kicks a football. | Velocity from ‘O’ changes to ‘u’ |
| 2. Second player kicks the football towards the goal. | Velocity changes again |
| 3. The goalkeeper collects the football. | Velocity becomes O |
| 4. Goalkeeper kicks it towards a player Of his team | Change in velocity takes place |
The velocity of football changed four times.
3. Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.
Ans. When the tree’s branch is shaken vigorously the branch attain motion but the leaves stay at rest. Due to the inertia of rest, the leaves tend to remain in its position and hence detaches from the tree to fall down.
4. Why do you fall in the forward direction when a moving bus brakes to a stop and fall backwards when it accelerates from rest?
Ans. When a moving bus brakes to a stop: When the bus is moving, our body is also in motion, but due to sudden brakes, the lower part of our body comes to rest as soon as the bus stops. But the upper part of our body continues to be in motion and hence we fall in forward direction due to inertia of motion.
When the bus accelerates from rest we fall backwards: When the bus is stationary our body is at rest but when the bus accelerates, the lower part of our body being in contact with the floor of the bus comes in motion, but the upper part of our body remains at rest due to inertia of rest. Hence we fall in backward direction.
NCERT Textbook Pages 126–127
1. If action is always equal to the reaction, explain how a horse can pull a, cart?
Ans. The third law of motion states that action is always equal to the reaction but they act on two different bodies.
In this case the horse exerts a force on the ground with its feet while walking, the ground exerts an equal and opposite force on the feet of the horse, which enables the horse to move forward and the cart is pulled by the horse.
2. Explain, why is it difficult for a fireman to hold a hose, which ejects a large amount of water at a high velocity.
Ans. The water that is ejected out from the hose in the forward direction comes out with a large momentum and equal amount of momentum is developed in the hose in the opposite direction and hence the hose is pushed backward. It becomes difficult for a fireman to hold a hose which experiences this large momentum.
3. From a rifle of mass 4 kg, a bullet of mass 50 g is fired with an initial velocity of 35 m/s. Calculate the initial recoil velocity of the rifle.
Ans. (m1) Mass of rifle = 4 kg (m2) Mass of bullet = 50 g = 0.05 kg
(v2) Velocity of bullet = 35 m/s (v1) Recoil velocity of rifle = ?
According to the law of conservation of momentum
Momentum of rifle = momentum of bullet
4. Two objects of masses 100 g and, 200 g are moving along the same line and direction with velocities of 2 m/s and 1 m/s respectively.
They collide and after the collision the first object moves at a velocity of 1.67 m/s. Determine the velocity of the second object.
Ans. m1 = 100 g = 0.1 kg m2 = 200 g = 0.2 kg
u1 = 2 m/s u2 = 1 m/s
After collision v1 = 1.67 m/s v2 = ?
m1u1 + m2u2 = m1v1 + m2v2
Questions from NCERT Textbook
1. 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.
Ans. When an object experiences a net zero external unbalanced force, in accordance with second law of motion its acceleration is zero. If the object was initially in a state of motion, then in accordance with the first law of motion, the object will continue to move in same direction with same speed. It means that the object may be travelling with a non-zero velocity but the magnitude as well as direction of velocity must remain unchanged or constant throughout.
2. When a carpet is beaten with a stick, dust comes out of it. Explain.
Ans. The carpet with dust is in state of rest. When it is beaten with a stick the carpet is set in motion, but the dust particles remain at rest. Due to inertia of rest the dust particles retain their position of rest and falls down due to gravity.
3. Why is it advised to tie any luggage kept on the roof of a bus with a rope?
Ans. In moving vehicle like bus, the motion is not uniform, the speed of vehicle varies and it may apply brake suddenly or takes sudden turn. The luggage will resist any change in its state of rest or motion, due to inertia and this luggage has the tendency to fall sideways, forward or backward.
To avoid the fall of the luggage, it is tied with the rope.
4. 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.
Ans. (c) there is a force on the ball opposing the motion.
5. A truck starts from rest and rolls down a hill with a constant acceleration. It travels a distance of 400 m in 20 s. Find its acceleration. Find the force acting on it if its mass is 7 tonnes (Hint : 1 tonne = 1000 kg).
Ans. u = 0 m/s m = 7 tonnes
s = 400 m = 7 x 1000 kg
t = 20 s = 7000 kg
a = ? F = ?
6. A stone of 1 kg is thrown with a velocity of 20 ms–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?
7. 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) the net accelerating force;
(b) the acceleration of the train; and
(c) the force of wagon 1 on wagon 2.
Ans. (a) The net accelerating force = Force exerted by the engine – friction force
= 40000 N – 5000 N = 35000 N
= 35000 N
(b) The acceleration of the train (a) = ?
F = 35000 N
Mass of 5 wagons pulled by engine = 5 × 2000 = 10000 kg F = ma 35000 = 10000 × a
(c) The force of wagon 1 on wagon 2
F = ? Mass of wagon 2 → (2000 × 4) a = 3.5 m/s2 F = ma
= 8000 × 3.5 = 28000 N
8. 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 ms–2?
Ans. mass = 1500 kg
a = –1.7 m/s2 F = ? F = m × a
= 1500 × (– 1.7) = – 2550 N
The force between the vehicle and road is – 2550 N.
9. What is the momentum of an object of mass m, moving with a velocity v?
(a) (mv)2 (b) mv2 (c) 1/2 mv2 (d) mv Ans. (d) mv
10. Using a horizontal force of 200 Ar. we intend to move.a wooden cabinet across a floor at a constant velocity, Wl.ot is the friction force that will be exerted on the cabinet?
Ans. As the wooden cabinet moves across the floor at a constant velocity and the force applied is 200 . Hence the frictional force that will be exerted on the cabinet will be less than 200 N.
11. 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?
Ans. Mass of the objects m1 = m2 = 1.5 kg
Velocity of first object v1 = 2.5 m/s
Velocity of second object v2 = – 2.5 m/s
Momentum before collision = m1v1 = m2v2
= (1.5 × 2.5) + (1.5 × –2.5) = 0
Momentum after collision = m1 + m2 = 1.5 + 1.5 = 3.0 kg
After collision v = ?
According to law of conservation of momentum
Momentum before collision = Momentum after collision
0 = 3 × v v = 0
12. 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.
Ans. The mass of truck is too large and hence its inertia is too high. The small force exerted on the truck cannot move it and the truck remains at rest. For the truck to attain motion, an external large amount of unbalanced force need � to be exerted on it.
13. 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 at 5 ms–1. Calculate the change of momentum occurred in the motion of the hockey ball by the force applied by the hockey stick.
Ans. Mass of ball m = 200 g = 0.2 kg
Initial speed of ball u = 10 m/s
Final speed of ball v = – 5 m/s
Initial momentum of the ball = mu
= 0.2 kg x 10 m/s = 2 kg m/s
Final momentum of the ball = mv
= 0.2 kg x (_ 5 m/s) = – 1 kg m/s
Hence, change in momentum = Difference in the momentum
=2 – (–1) = 2 + 1 = 3kg m/s
14. 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.
∴ The penetration distance of the bullet in the wooden block = 2.25 m.
Magnitude of force F = ma
15. An object of mass 1 kg travelling in a straight line with a velocity of 10 msr’ 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.
Ans. m1 = 1 kg
v1 = 10 m/s
Mass of wooden block = 5 kg
m2 = 5 kg + 1 kg (combined object) = 6 kg
Velocity of combined object = v2 = ?
p1 and p2 = ?
Momentum before impact p = m1v1
= 1 × 10 = 10 kg m/s
∴ Momentum before impact = Momentum after impact
16. An object of mass 100 kg is accelerated uniformly from a velocity of 5 ms–1to 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.
Ans. m = 100 kg
u = 5 m/s v = 8 m/s t = 6s p1 = ? p2 = ? F = ?
Initial momentum p1 = mu
= 100 × 5 = 500 kg m/s
Final momentum p2 = mv
= 100 × 8 = 800 kg m/s
Force exerted on the object F = ma
17. 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 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 on 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.
Ans. Rahul gave the correct reasoning and explanation that both the motorcar and the insect experienced the same force and a change in their momentum. As per the law of conservation of momentum.
When 2 bodies collide:
Initial momentum before collision = Final momentum after collision
m1u1 + m2u2 = m1v1 + m2v2
The equal force is exerted on both the bodies but, because the mass of insect is every small it will suffer greater change in velocity.
18. How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 ms–2,
Ans. Mass of dumb-bell = 10 kg
Height, h = 80 cm = 0.8 m
a = 10 m/s2 u = 0 v2 – u2 = 2 as
v2 – (0)2 = 2 × 10 × 0.8 v2 = 16 v = 4 m/s
Momentum p = mv = 10 × 4 = 40 kgm/s
CONCEPT’S QUESTIONS
1. State two effects of force.
2. Scientist who first conducted experiment to form the base for Newton’s first law of motion.
3. If first law of motion holds true, why does a ball rolling on ground stop on its own?
4. What would happen if there was no friction on the Earth?
5. What would happen if gravitational force of the Sun suddenly vanishes?
6. What did Galileo observe by placing two inclined planes facing each other and rolling down a marble ball from top end of one of them?
7. What is the negative effect of friction on your shoe soles?
8. You are applying force on the pan of single pan weighing balance and the pointer points to 100 g. What is the force in newtons applied by you?
9. An athlete always runs some distance before taking a jump. Why?
10. A cricket ball of mass 70 g moving with a velocity of 0.5 m/s is stopped by a player in 0.5 s. What is the force applied by the player to stop the ball?
11. In a cricket match, why does a player lower his hands slightly while catching the ball?
12. Two cars having masses in the ratio 4 : 5, accelerate in the ratio 2:3. Find the ratio o forces exerted by each of them.
CONCEPT’S SAMPLE QUESTIONS
1. What do you mean by law of conservation of momentum?
2. Why do roads on mountains have inward inclination at sharp turns?
3. Why is it dangerous to jump out of a moving bus?
4. How do safety belts of cars help in preventing accidents?
5. Explain how momentum gets conserved in collision of two bodies?
6. How are Newton’s three laws of motion related?
7. Explain inertia and momentum in detail.
8. Define force and its various types. What is its unit?
9. Give three examples exhibiting inertia in our daily life
10. What change will a force bring in a body?
11. From a rifle of mass 5kg, a bullet of mass 50gram is fired with an initial velocity of 50m/s. Calculate the initial recoil velocity of the rifle.
12. Explain how Newton�s second law of motion is used in sports?
13. Why does one get hurt on jumping from a great height to the floor?
14. What is a balanced force?
CONCEPT’S SAMPLE PAPER
(To Check your preparation)
MAXIMUM TIME: 40 MINUTES MAXIMUM MARKS: 25 marks
1. Why do passengers tend to fall sideways when the bus takes a sharp u turn? (2 marks)
2. Why should a passenger hold on to prevent himself from swaying in a turning bus? (2 marks)
3. Why do passengers tend to fall back when it starts suddenly? (2 marks)
4. Why do passengers jumping out of a rapidly moving bus fall forward with his face downwards, if he does not run forward? (2 marks)
5. Why does a passenger jumping out of a rapidly moving bus fall forward with his face downwards? (2 marks)
6. Why can dust be removed by shaking it, or beating it by a carpet? (2 marks)
7. Why does a bullet when fired against a glass window pane make a hole in it, and the glass pane will smash it? (2 marks)
8. Why does an athlete take a longer jump if he comes running from a distance than when he jumps suddenly from the take-off line? (2 marks)
9. What happens when you shake a wet piece of cloth? Explain, why? (2 marks)
10. Why is it advised to tie a rope on the luggage while you travel by the bus? (2 marks)
11. How does a boat move forward into the water when the boatman presses one end of the pole against the ground? (2 marks)
12. Why is it difficult for a fireman to hose, which ejects large amount of water at a high velocity? (3 marks)
Multiple Choice Questions (MCQ)
1. The S.I. unit of force is
I. Kgm/s II. Kgm/s2 III. Newton IV. Newton-meter
2. What do we get by the product of mass and velocity?
I. Force II. Inertia III. Momentum IV. Newton
3. The rate of change of momentum of an object is proportional to
I. Mass of the body II. Velocity of the body III. Net force applied on the body IV. None of these
4. If two balls of same masses are dropped on sand, the depths of penetration is same if
I. Heavier ball is dropped faster than lighter ball II. Lighter ball is dropped faster than heavier ball
III. The product ‘mv’ is same for both bodies IV. None of these
5. A coin placed on a card (rested at the edges of the glass) remains at rest because of
I. Inertia of rest II. Two forces act on the coin which balance each other
III. No unbalanced force acts on it IV. All of these
6. A force of 50N moves a body,
I. Friction force exerted on the body is less than 50N II. Friction force exerted on the body is more than 50N
III. None of these IV. Both of I and II
7. A fielder giving a swing while catching a ball is an example of
I. Inertia II. Momentum III. Newton’s II law of motion IV. Newton’s I law of motion
8. Action and reaction forces
I. Act on the same body II. Act on different bodies III. Act in same direction IV. Both I and III
9. When we pedaling the bicycle it stops because
I. The earth’s gravitational force acts on it II. It is not accelerated
III. No unbalanced force acts on it IV. Frictional force acts on it
10. A football and a stone has same mass
I. Both have same inertia II. Both have same momentum
III. Both have different inertia IV. Both have different momentum