Newton's Laws of Motion

the relation between force and motion id described in Newtons three laws of motion. These laws are very simple statements and enable us to describe the future (or past) motion of body if we know the forces acting on it.

1. Newton’s Laws of Motion Peter Huruma Mammba Department of General Studies DODOMA POLYTECHNIC OF ENERGY AND EARTH RESOURCES MANAGEMENT (MADINI INSTITUTE) –DODOMA [email protected] m

2. Laws of motion The Newton’s laws of motion are the principles of dynamics . Dynamics means; the relationship of motion to the forces that cause it.

3. Laws of motion… The dynamic principles are the foundation of classical mechanics which also called Newtonian Mechanics .

4. Laws of motion… Since these dynamic principles are phrased in terms of force and mass , it will be helpful to have some understanding of these two concepts before dealing with Newton’s laws of motion.

5. The Concept of Force Force is a push or pull acting on a body. When force involves direct contact between two bodies , we call it a Contact force .

6. Force… The force of gravitation attraction that the Earth exert on your body is called weight . The net force is the vector sum of all the forces acting on the object.

7. Force… Force has magnitude as well as direction ,it is a vector quantity . The SI unit of magnitude of force is Newton (N).

8. Force… The fundamental forces in nature are all field forces: Gravitational force between objects Electromagnetic forces between the charges

9. Force… Strong forces between subatomic particles Weak forces that arises in a certain radioactive decay processes

10. Force… In classical Mechanics , we are concerned only with Gravitational force and Electromagnetic force .

11. M ass Mass defines as the quantity of matter contained in the body. More precisely, mass is a measure of the inertia of the body. i.e. the more mass a body has, the harder it is to change its state of motion.

12. Mass should not be confused with weight Mass and weight are two different quantities . The weight of an object is equal to the magnitude of the gravitational force exerted on the object and varies with location. For example , a person weighing 180 lb on the Earth weighs only about 30 lb on the Moon .

13. M & W are different quantities… On the other hand, the mass of an object is the same everywhere : an object having a mass of 2 kg on the Earth also has a mass of 2 kg on the Moon.

14. Inertia Is the tendency of a body to maintain its state of rest or of uniform motion in a straight line. Object do not change their state of motion unless acted upon by some net external force.

15. Inertia… The inertia of the body depends upon its mass. The greater the mass of the body, the greater is its inertia Both mass and inertia are measured in the same units.

16. Types of inertia Inertia of the body is of three type Inertia of rest Inertia of motion Inertia of direction

17. Inertia of rest This is the resistance of the body to change its state . For example when a train suddenly starts, the passenger sitting inside tends to fall backward. It is because the lower part of his body starts moving with the train while the upper part tends to be at rest due to inertial at rest.

18. Inertia of motion This is the resistance of the body to change its state of motion. For example. When a bus suddenly stops, a passengers siting in it tends to fall forward. It is because the lower part of the body comes to rest while the upper part of the body tends to remain in motion due to inertia of motion

19. Inertia of direction This is the resistance of the body to change its direction of motion . In other words a body will continue to move in the same straight line unless some external force tends to change its direction.

20. 1 st Law of Motion (Law of Inertia) State that Every body will continues in it state of rest or uniform motion in a straight line unless it is compelled by some external force to change the state

21. Law of Inertia… The following conclusion can be drawn from this law:- ( i ) If a body is at rest or moving with constant velocity, the net force acting on the body is zero.

22. Law of Inertia… (ii) when you move an object on the ground with constant velocity, the force you exert is not zero. But the net force is zero because the fractional force on the object is equal and opposite to the force you exert on the object.

23. Law of Inertia… (iii) If a body is moving with a constant speed in a straight line, then in order to change its direction , force has to be applied on the body.

24. Law of Inertia… (iv) If a body is moving with a constant speed in a circle, then force is required to keep it going in circular path. This is due to change in direction continuously.

25. Newton's 1 st Law and You Don’t let this be you. Wear seat belts. Because of inertia, objects (including you) resist changes in their motion. When the car going 80 km/hour is stopped by the brick wall, your body keeps moving at 80 m/hour.

26. 2 nd Law of Motion F = m x a

27. 2 nd law of Motion State that the rate of change of momentum of a body with time is directly proportional to the net external force applied on it and the change takes place in the direction of force.

28. 2 nd law of Motion If is the momentum of the body and is the net external force acting on the body , then according to newton’s 2 nd law of motion ; Or where k = 1  

29. 2 nd law of Motion but mass of an object does not change. m but = Magnitude of force,  

30. 2 nd law of Motion If is the resultant acceleration produced in 3D and and are the magnitude of the components of acceleration along x- axis , y-axis and z- axis respectively then;  

31. 2 nd law of Motion If , and are the components of force along x- axis , y- axis and z-axis respectively, then,  

32. 2 nd law of Motion When mass is in kilogram (Kg) and acceleration is in , the unit of force is in Newton (N) . One newton is equal to the force required to accelerate one kilogram of mass at one meter in a second.  

33. 3 rd Law of Motion

34. 3 rd Law of Motion State that For every action, there is an equal and opposite reaction.

35. 3 rd Law According to Newton , whenever objects A and B interact with each other, they exert forces upon each other. When you sit in your chair, your body exerts a downward force on the chair and the chair exerts an upward force on your body.

36. 3 rd Law There are two forces resulting from this interaction - a force on the chair and a force on your body. These two forces are called action and reaction forces.

37. Action - Reaction When the rocket fuel is ignited, a hot gas is produced. As the gas molecules collide with the inside engine walls, the walls exert a force that pushes them out of the bottom of the engine.

38. Action – Reaction… This downward push is the action force. The reaction force is the upward push on the rocket engine by the gas molecules. This is the thrust that propels the rocket upward.

39. Other examples of Newton’s Third Law The baseball forces the bat to the left (an action); the bat forces the ball to the right (the reaction).

40. 3 rd Law Consider the motion of a car on the way to school. A car is equipped with wheels which spin backwards. As the wheels spin backwards, they grip the road and push the road backwards.

41. Example 1 What force is required to accelerate 2000 Kg car from 5 m/s to 25 m/s in a time of 5 seconds?  

42. Assignment 1 The mass of an elevator (lift) is 500 Kg. calculate the tension in the cable of the elevator when the elevator is ( i ) stationary (ii) ascending with an acceleration of 2 m/s (iii) descending with the same acceleration. Take g = 9.8 m/s/s.

43. Assignment 2 A particle of mass 0.4 Kg moving with a constant speed of 10 m/s to the north is subjected to a constant force of 8 N directed towards the south for 30 s. Take the instant the force is applied to be t = 0, the position of the particle at that time to be x = 0 and predict position of the particle at t = -5 s, 25 s, 100 s.

44. Assignment 3 Two blocks, A of mass m and B of mass 3 m, are side by side in contact with each other. They are pulsed along a smooth floor under the action of a contact force f applied to A. Find ( i ) accelerations of the blocks (ii) The force exerted on B by A.

45. Assignment 4 A 68 Kg man is standing on the floor of a lift. Calculate the apparent weight of the man when the lift is ( i ) at rest (ii) moving upward with constant speed (iii) moving upward with an acceleration of 1m/s/s (iv) moving downward with an acceleration of 1 m/s/s.

46. Assignment 5 A monkey of mass 40 Kg climbs on a rope which can stand a maximum tension of 600 N. In which of the following cases the rope will break: If monkey climbs up with an acceleration of 6 m/s/s If monkey climbs down with an acceleration of 4 m/s/s.

47. Assignment 5 … (iii) If monkey clims up with a uniform speed of 5 m/s (iv) If monkey falls down the rope nearly freely under gravity. Ignore the mass of the rope and take g = 9.8 m/s/s.