CBSE Class 11 Physics Newtons Laws Of Motion Notes Set D

Newton’s Laws of Motion

Main points

1.Newton’s first law of motion states that everybody continues to be in its state of rest or of uniform motion unless it is acted by an external force or it can also be stated as ‘‘ If external force on a body is zero, its acceleration is zero.”

2.Momentum (p) of a body is the product of mass (m) and velocity (v): P=mv

3. Newton’s Second law of motion : It states that the rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which force acts.

Thus F= k dp/dt= k ma

The SI unit of force is: 1N= 1kgms^-2

√ The second law is consistent with the First law (F=0 implies a=0)

√It is a vector equation 

√ It is applicable to a particle, and also to a body or a system of particles, provided F is the total external force on the system and a is the acceleration of the system as a whole.

√ F at a point at a certain instant determines acceleration at the same point at that instant.Acceleration at an instant does not depend on the history of motion’

√ Force is not always in the direction of motion .Depending on the situation F may be along V, opposite to v, normal to v, or may make some other angle with v. In every case it is parallel to acceleration.

√ If v=0 at an instant, i.e., if a body is momentarily at rest, it does not mean that force or acceleration are necessarily zero at that instant. For ex: When a ball thrown upward reaches its maximum height, but the force continues to be its weight ‘mg‘ and the acceleration is ‘g’ the acceleration due to gravity.

4. Impulse is the product of force and time which equals change in momentum. The notion of impulse is useful when a large force acts for a short time to produce a measurable change in momentum. Since the time of action of the force is very short, one can assume that there is no appreciable change in the position of the body during the action of the impulsive force. 

(i) Impulse = F X Δt = m (v- u)

(ii) Unit of measurement of Impulse is Ns

5.Newton’s third law of motion:

“To every action, there is an equal and opposite reaction.”

The law can be stated:

Forces in nature always occur between pairs of bodies. Force on a body A by a body B is equal and opposite to the force on the body B by A.

√ Action and reaction forces are simultaneous forces.

√ There is no cause-effect relation between action and reaction.

√ Any of the two mutual forces can be called action and the other reaction.

√ Action and reaction can act on different bodies and so they cannot be cancelled out.

√ The internal action and reaction forces between parts of a body do however sum to zero.

√ The equation mg = R for a body on a table is true only if the body is in equilibrium. The two forces mg and R can be different. The equality of mg and R has no connection with the third law of motion.

√ FAB = - FBA

6. Law of conservation of momentum:

“The total momentum of an isolated system of particles is conserved. “This law follows from the second law of motion.

7. Friction

√ Frictional force opposes relative motion between two surfaces in contact.

√ It is the component of the contact force along the common tangent to the surface in contact.

√ Static frictional force‘ f_s‘oppose impending relative motion: kinetic frictional force ’ f_k ‘opposes actual relative motion.

• They are independent of the area of contact.

• They satisfy the following approximate 

whereμs(coefficient of static friction ) and μk( Coefficient of kinetic friction) are constants characteristic of the pair of surfaces in contact.

• μk ‹ μs

• Static frictional force is a self-adjusting forceup to its

limit μsN (fs≤μs N)

Answer the following questions. Each question carries 1 mark.

1. State the Galileo’s law ofinertia?

2. Define force? Give the SI unit of force.

3. Give the Dimensional formula of force.

4. State Newton’ first law of motion.

5. Define linear Momentum of a body. Give the SI unit of it.

6. Give the Dimensional formula of linearmomentum. Is it a scalar or a Vector quantity?

7. State the law of Conservation of linear momentum.

8. Express Newton’s second law of motion in the vector form

9. What is meant by Impulse? Give the SI unit of it.

10. Give the Dimensional formula of Impulse.

11. Is weight a force or a mass of a body? Name the unit in which force is measured.

12. Name some basic forces in nature.

13. Constant force acting on a body of mass 3 kg changes its speed from 2 m/sec to 3.5 m/sec.If the direction of motion of the body remains u changed, what is the magnitude and direction of motion of the force?

14. A charged comb is able to attract bits of paper against the huge gravitational pull of the earth. What does it prove?

15. What is centripetal Force? Give the expression for finding the centripetal force.

16. Define force of friction .What is the cause friction?

17. Define coefficient of kinetic friction

18. Define angle of friction

19. Define angle of Repose

20. Compare μkwithμs. Is it reasonable to expect the value of coefficient of friction to exceed unity?

21. State Newton’s third law of motion.

Answer the following. Each question carries 2 marks

2.A force acts for 20 sec on a body of mass 10 kg after which the force ceasesand the body describes 50 m in the next 10 secs. Find the magnitude of the force.

3.A body of mass 5 kg is acted upon by two perpendicular forces 8 N and 6 N. Find the magnitude and direction of the acceleration.

4.A constant retarding force of 50 N is applied to a body of mass 10 kg moving initially with a speed of 15m/sec. How long the body does takes to stop.

5.What is linear momentum of a body how is it related to impulse?

6.Write two applications of the concept of Impulse.

7. What do you mean by free-body diagram?

8. Why does a cricket player lower his hands while catching a ball?

9. How does the spring balance weigh the weight of a body?

 Answer the following. Each question carries 3 marks.

1. Show that Newton’s second law is the real law of motion

2. State and prove the law of conservation of linear momentum

3. A force 10 N acts on a body for 3 X 10 ^-6sec calculate the impulse. If mass of the body is 5 g . Calculate the change in velocity.

4. A man weighs 60 kg. He stands on a weighing machine in a lift, which is moving

(a) Upwards with a uniform speed of 6 m/s

(b) Downward with a uniform acceleration of 6m/s².

(c) Upwards with a uniform acceleration of 6 m/s²

What would be the reading of the scale in each case? What would be the reading if the lift mechanism fails, and fall freely?

5. A shell of mass 20 g is fired by a gun of mass 100 kg. If the muzzle speed of the shell is 80 m/s. What is the recoil speed of the gun? What is the recoil speed of the gun?

6. Given the magnitude and direction of the net force acting on

(a) A drop of rain falling down with a constant speed

(b) A cork of mass 10 g floating on water

(c) A kite skilfully held stationery in the sky

(d) A car moving with a constant velocity of 30 km/hron a rough road.

10. Two masses m1and m2 are connected at the ends of a light inextensible string that passes over frictionless pulley. Find the acceleration, tension in the string and thrust on the pulley when the masses are released.

(e) A high-speed electron in space far from all gravitating objects and free of electric and magnetic fields.

7.A pebble of mass 0.05 kg is thrown vertically upwards. Give the direction

and magnitudeof the net force on the pebble

(a) During its upward motion

(b) During its downward motion

(c) At the highest point where it is momentarily at rest.Do your answers alter if the pebble were thrown at an angle of 45˚ with the horizontal direction?

8. What are the laws of limiting friction?

9. State and prove the law of conservation of linear momentum

10. Discuss the variation of frictional force with the applied force on a body.

Also show the variation by plotting a graph between them.

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