Dynamics JPJC Notes

1 JURONG PIONEER JUNIOR COLLEGE 9749 H2 PHYSICS DYNAMICS ______________________________________________________________________ Content (1) Newton's laws of motion (2) Linear momentum and its conservation Learning Outcomes Students should be able to: (a) state and apply each of Newton’s laws of motion (b) show an understanding that mas s is the property of a body which resists change in motion (inertia) (c) describe and use the concept of weight as the force experienced by a mass in a gravitational field (d) define and use linear momentum as the product of mass and velocity (e) define and use impulse as the product of force and time of impact (f) relate resultant force to the rate of change of momentum (g) recall and solve problems using the relationship F = ma , appreciating that resultant force and acceleration are always in the same direction (h) state the principle of conservation of momentum (i) apply the principle of conservation of m omentum to solve simple problems including inelastic and (perfectly) elastic interactions between two bodies in one dimension (knowledge of the concept of coefficient of restitution is not required) (j) show an understanding that, for a (perfectly) elastic collision between two bodies, the relative speed of approach is equal to the relative speed of separation (k) show an understanding that, whilst the momentum of a closed system is always conserved in interactions between bodies, some change in kinetic energy usually takes place.

2 Introduction_________________________________________________________ If you see the velocity of an object change in either magnitude or direction, you know that something must have caused that change (or acceleration). An interaction that can cause an acceleration of a body is called a force, which is loosely speaking, a push or a pull on the body. The relationship between a force and the acceleration it causes was first understood by Isaac Newton (1642 – 1727). The study of the relationship is called Newtonian mechanics. We shall focus on its 3 primary laws of motion. Newtonian mechanics does not apply in the following situations:  When the speeds of the interacting bodies are very large (i.e. approaching the speed of light). In this case, Einstein’s special theory of relativity replaces Newtonian mechanics.  When the interacting bodies are on the atomic scale. In this case, Quantum mechanics replaces Newtonian mechanics. Physicists now view Newtonian mechanics as a special case of these two more comprehensive theories. Linking Kinematics and Dynamics In Kinematics, when we look at describing the motion of objects, we are concerned only with how the displacement, velocity and acceleration of the objects change with time. We then try to answer questions like: a) How far has the object moved from the starting/reference point? b) How long does the object take to move from point A to point B? c) How fast must the object move to travel from point A to point B within a certain time interval? In Dynamics, we will discuss the cause of motion using two quantities: force and mass, and study their relationships to the motion of objects. We then try to answer questions like: a) Why does something move? b) Why does something CONTINUE to move? c) What causes something to STOP once it is moving? 1 Newton’s laws of motion______________________________________________ (a) State and apply each of Newton’s laws of motion. (b) Show an understanding that mass is the property of a body which resists change in motion (inertia). 1.1 Newton’s first law of motion  Suppose you send a book sliding across a carpet by applying a horizontal force to it with your hand. After you stop pushing, the book slows down and comes to rest soon after. If you want it to continue sliding, you will have to keep pushing it across the Sir Isaac Newton Sir Isaac Newton

3 carpet. How about if you now give a push to the book on a frozen lake of ice? In this case, the book would probably slide much further on its own although eventually it will still come to rest.  What is it that causes the book to come to rest in these two instances? It is the friction between the book and the surface; the friction between the book and the carpet is much higher than that between the book and the frozen lake.  If we can eliminate friction completely, the book will never slow down, and we would need no force at all for the book to keep moving with constant velocity.  Most moving bodies on Earth visible to us tend to come to rest in the absence of a n applied force. This is because moving bodies on Earth are continuously subjected to effects of resistive forces, be it from the ground, air or even between mechanical parts.  Therefore it is a common misconception that a force must always be applied to keep a body moving at constant velocity.  Newton’s first law of motion states that: A body will continue in its state of rest or uniform motion in a straight line unless a net external force acts on it.  Motion that is uniform in a straight line implies that velocity is constant . In other words, there is no acceleration.  Newton’s first law of motion tells the effects of what a force does. A force when applied on an object causes it to accelerate (change in velocity).  We may have more than one force acting on the object. As such, we consider the effect of the resultant force acting on the object.  Hence, if an object is at rest or moving with constant velocity, EITHER no force acts on it, OR the resultant force acting on it is zero.  Newton’s first law of motion is often called the law of inertia. The inertia of a body is the reluctance of a body to change its state of rest or motion. The mass of a body is a measure of its inertia . The larger the mass, the greater the inertia. It is more difficult to kick a large rock and expect it to move compared to doing the same to a small pebble.  Mass is the property of a body which resists change in motion (inertia).  To change the state of motion (i.e. velocity) of an object, a force (push or pull) must be applied to the object. However, the state of motion may remain unchanged even when a force is applied to the object.  Inertia can be used to explain why a force is needed to:  move a stationary object,  stop a moving object,  change the direction of an object moving in a straight line.

4 (c) describe and use the concept of weight as the force experienced by a mass in a gravitational field  When an object is brought from place to place, its mass remains the same. However, its weight may vary considerably from place to place. While it is true that you will weigh less if you have less mass, this cannot account fully for the difference. For example, you will weigh six times lighter on the Moon than on the Earth. This is not because you have lost mass. You still have the same mass. The difference in weight arises because of the difference in the gravitational field strength of the Earth and that of the Moon. The weight of a body is the gravitational force exerted on it by a gravitational field.  SI Unit : newton (N)  Mass is a scalar quantity, while weight is a vector quantity.  The direction of weight is always in the direction of the gravitational field strength. In the context of Earth, weight will always point towards the centre of the Earth. 1.2 Newton’s second law of motion (d) Define and use linear momentum as the product of mass and velocity. (e) Define and use impulse as the product of force and time of impact. (f) Relate resultant force to the rate of change of momentum. (g) Recall and solve problems using the relationship F = ma, appreciating that resultant force and acceleration are always in the same direct