Newton s Laws of Motion. (10 Marks) Main points

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1 Newton s Laws of Motion (10 Marks) 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.

2 (i) Impulse = F X t = 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. F AB = - F BA 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 laws: f s (f s ) max =μ s R f k = μ k R

3 whereμ s (coefficient of static friction ) and μ k( Coefficient of kinetic friction) are constants characteristic of the pair of surfaces in contact. μ k μ s Static frictional force is a self-adjusting forceup to its limit μ s N (f s μ s 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 μ k withμ s. 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 1.What do you mean by inertial frame of reference? Why is it so important? Give an example of inertial frame of reference.

4 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? 10. Two masses m 1 and m 2 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. 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 10-6 sec 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/s 2. (c) Upwards with a uniform acceleration of 6 m/s 2 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.

5 (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. Answer the following questions. Each question carries 5 marks. 1. Show that Newton s second law is the real law of motion. 2. (a)state Newton s second law of motion. (b) What is the acceleration of the block and trolley system sown in fig. if the coefficient of kinetic friction between the trolley and the surface is 0.04? What is the tension in the string? Take g = 10 m/s 2. Neglect the mass of the string. 20 kg T T 30kgf

6 3. (a) State Newton s laws of motion (b) A machine gun has a mass of 20 kg. It fires 35 g bullets at the rate of 400 bullets per second with a speed of 400m/s.What force must be applied to the gun to keep it in position? 4. (a) State the principle of conservation of momentum. (b) A hammer of mass 1 kg moving with a speed of 6 m/sstrikes a wall and comes to rest in 0.1 s, Calculate (i) (ii) (iii) The impulse of force The retardation of the hammer, and The retarding force that stops the hammer. 5. What is meant by banking or roads? Discuss the motion of a car on a banked road. Main points 1. Work is said to be done by a force when the force produces a displacement in the body on which it acts in any direction except perpendicular to the direction of force. 2. W = FS cosѳ 3. Unit of measurement Work done is Joule or Nm 4. Work done is a scalar quantity. 5. If a graph is constructed of the components FcosѲ of a variable force, then the work done by the force can be determined by measuring the area between the curve and the displacement axis. 6. Energy of a body is defined as the capacity of the body to do work. 7. Energy is a scalar quantity. 8. The Dimensional formula of Energy is same as Work and is given by ML 2 T The SI unit of Energy is same as that of Work. i.e., Joule.

7 10. The work-energy theorem states that the change in kinetic energy of a body is the work done by the net force on the body. K f - K i =W net 11. Momentum of a body is related to Kinetic Energy by P = 2m E k 12. A force is said to be conservative if work done by or against the force in Movinga body depends only on the initial and final positions of the body not on the nature of the path followed between the initial and final positions. For ex: Gravitational Force,Elastic Force, Electrostatic Force etc. 13. A force is said to be non-conservative if work done by or against the force in moving a body depends upon the path between the initial and final positions. 14. For a conservative force in one dimension, we may define potential energy Function U(x) such that F(x) = -du(x)/dx x f Or U i -U f = F(x) dx x i 15. The principle of conservation of mechanical energy states that the total mechanical energy of a body remains constant if the only forces that act on the body are conservative. 16. The gravitational potential energy of a particle of mass m at a height x above the earth s surface is U(x)=mgx Where the variation of g with height is ignored. 17. Theelastic potential energy of a spring of force constant k and extension x is U(x) = ½ k x Power is defined as the time rate of doing work. 19. Average Power is given by P av =W/t 20 Power is a scalar quantity, P= F.v = FvcosѲ, P = dw/dt 21. SI unit of Power is Watt

8 22. The Dimensional Formula of Power is M 1 L 2 T The Scalar or dot product of two vectors A and B is written as A.B and is a scalar quantity given by : A.B = AB cosѳ where Ѳ is the angle between A and B. It can be positive, negative or zero depending upon the value of the scalar product of the two vectors can be interpreted as the product of magnitude of one vector and the component of the other vector in the direction of the first vector. For unit vector I^.i^=j^.j^=k^.k^= 1 and i^.j^= j^.k^=k^.i^=0 24.For two bodies, the sum of the mutual forces exerted between them is zero from Newton s third law, F 12 + F 21 =0 But the sum of the work done by the two forces need not always cancel. i.e., W12 + W21 0 However, it may sometimes be true. 25.Elastic collision is a collision in which both momentum and kinetic energy are conserved 26. In inelastic collision momentum is conserved but kinetic energy is not conserved. 27.In a collision between two bodies the Coefficient of restitution can be defined as the ratio between the velocity of separation to the velocity of approach i.e. e = velocity of separation /velocity of approach If e = 1 then the collision is perfectly elastic, if e=0, then the collision is perfectly inelastic. Answer the following questions.each question carries one mark. 1.Define work. How can you measure the work done by a force? 2. Write the Dimensional formula of work. Give its SI unit of measurement 3. Give examples of zero work done 4. A body is compelled to over along the x-direction by a force given by F= (2i^-2j^+k^) N What is the work done in moving the body? (i)a distance of 2m along x-axis (ii) a distance of 2m along y-axis.

9 5. What do you mean by a conservative force? Is frictional force a conservative force. 6. Define power. Is it a scalar or vector? 7. Define one electron volt 8. State work energy theorem 9. Compare 1kwh with electron volt 10. Two bodies of mass 1 kg and 4 kg have equal linear momentum. What is the ratio of their kinetic energies? 11. Distinguish between elastic and inelastic collision. 12. A light and a heavy body have the same momentum. Which one will have the greater kinetic energy? 13. When a ball is thrown up, the magnitude of its momentum decreases and then increases. Does this violate the law of conservation of momentum? 14. Define coefficient of restitution. 15. What is the amount of work done, when a body of mass m moves with a uniform speed v in a circle? Answer the following questions. Each question carries 2 marks. 1. Plot a graph showing the variation of Force (F) with displacement(x), if its force equation is given by F = -kxname at least four commonly used units of energy. 2. Differentiate between a conservative force and a non-conservative force. 3. What is Einstein s energy-mass equivalence relation? 4.A man whose mass is 75kg walks up 10 steps each 20 cm high, in 5 sec. Find the power he develops Take g= 10m/s2. 5. A block of mass 2 kg moving at a speed of 10 m/s accelerates at 3 m/s 2 for 5 sec. Compute the final kinetic energy. 6. The sign of work done by a force on a body is important to understand.state carefully if he following quantities are positive or negative. (a)work done by a man in lifting a bucket out of a well by means of a rope tied to the bucket. (b) Work done by gravitational force in the above case.

10 (c) Work done by friction on a body sliding down an inclined plane (d) Work done by an applied force on a body moving on a rough horizontal plane with uniform velocity. 7. What happens to the potential energy of a body when the work done by the conservative force is positive? Answer the following. Each question carries 3 marks. 1. State and prove work-energy theorem 2. A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to k/r 2, where k is a constant. What is the total energy of the particle? 3. State and prove the law of conservation of energy. 4. Show that Potential energy y = mgh 5. Show that kinetic energy = ½ mv 2 6. Prove the law of conservation of energy at every point of the motion of a body under freefall. 7. Derive an expression to find the potential energy of a spring. 8. Plot graphs between K.E, P.E, and total energy of an elastic spring with displacement (x). 9. What is the power output of the sun if 4 x 10 9 kg of matter per second is converted into energy in the sun? 10. A body of mass 5kg initially at rest is moved by a horizontal force of 20 N on a frictionless table. Calculate the work done by the force in 10 seconds and prove that this equals the change in kinetic energy. 11. An engine pumps out 40 kg of water per second. If water comes out with a velocity of 3 m/sec, then what is the power of the engine? Answer the following questions. Each question carries 5 marks. 1. Discuss elastic collision in one dimensional motion. 2. Discuss the elastic collision in two dimension 3. Derive the expression for the work done by (i) Constant force and (ii) a variable force. 4. (a)what are conservative and non-conservative forces? Give examples. (b)a body of mass 5 kg is acted upon by a variableforce. The force varies with the distance covered by the body as shown in fig. What is the speed of the body when the body has covered 25 m. Assume that the body starts from rest?

11 10N Force 25 m Distance 5. A 10 kg ball and a 20 kg ball approach each other with velocities 20m/s and 10 m/s respectively. What are their velocities after collision if the collision is perfectly elastic. Also show that kinetic energy before collision is equal to kinetic energy after collision. 6. Starting with an initial speed v 0,a mass m slides down a curved frictionless track Arriving at the bottom with a speed v. From what height did it start? V0 h v 7. A ball dropped from a height of 8m hits the ground and bounces back to a height of 6m only. Calculate the frictional loss in kinetic energy.