Dynamics- Why do objects move as they do? What makes an object at rest, begin to move? What makes a body accelerate or decelerate?

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1 Dynamics- Why do objects move as they do? What makes an object at rest, begin to move? What makes a body accelerate or decelerate? What makes an object move in a circle?

2 Force A Force is simply a push or a pull. A Force gives energy to an object. What can that energy do? CHANGE the motion of an object. What do we call a CHANGE in the motion (speed or direction) of an object? ACCELERATION Forces are vectors with magnitude and direction. Not all objects will move when forces are applied to them. (push a wall!)

3 Measuring force One way to measure small forces is by use of a spring scale. As a push or pull is applied to the spring scale attached to a block (Or your fruit in the supermarket), the scale reads the measure of the force applied by stretching a spring calibrated in increments of force (Newtons or Dynes).

4 Newton s First Law of Motion Isaac Newton ( ) built off the ideas of Aristotle and Galileo regarding the relationship between force and motion. Aristotle claimed a moving object would come to rest if left alone. Galileo idealized the world to say if friction were removed, all moving objects would maintain their motion (speed and direction) and moving objects slow down only when a force is exerted on them.

5 Newton s First Law Newton s First Law of Motion is very close to Galileo s conclusions: Every body continues in its state of rest or uniform speed in a straight line unless acted on by a nonzero net force. The tendency of a body to maintain its state (rest or motion uniformly) is called inertia. Newton s First Law is often called the Law of Inertia.

6 Frames of Reference Newton s first law does not hold for all frames of reference. If you are fixed in a moving car and an object is resting on the dashboard, it may move toward you if the car accelerates though neither you nor anything else touched the cup to make it do that. Inertial Reference frames are those frames where Newton s first law DOES hold true. Most frames fixed on Earth are inertial. Reference frames where this law DOES NOT hold true are called noninertial reference frames.

7 Mass Newton used mass as synonym for quantity of matter. Quantity of matter is difficult to define. More precisely we say mass is the measure of inertia of an object. More mass = more inertia = more difficult to change motion. (Converse is true also)

8 Weight is NOT mass Though the mass of an object is a relatively fixed quantity, gravity is always present The force of gravity acting on a mass gives the object weight which has a magnitude and direction. Weight is a force. Mass responding to the force of gravity. Your mass on the moon vs your weight?

9 Newton s Second Law Newton s first law describes an object when NO NET force acts on it. What happens when there IS a NET FORCE? A net force may increase or decrease the speed of an object OR change its direction of motion. A net force gives rise to ACCELERATION. Greater the net force, greater the acceleration. F a

10 What about mass? The greater the mass of an object, the LESS the acceleration for the same net force. Mass and acceleration are inversely related. a 1 m

11 Newton s Second Law summed up The acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object. a F F ma m ΣF is the vector sum of all forces acting on the body which we call the Net Force.

12 Components and units of Forces Since a force is an action capable of accelerating an object, we need to look at each component of any given force separately. F ma x x F y ma y F z ma z In SI units, with mass in Kilograms, the unit of force is the Newton (N) where 1N = 1kg*m/s/s IN the cgs system, with mass in grams, the unit of force is the dyne where 1 dyne = 1g*cm/s/s

13 Ex1: Force to accelerate a fast car Estimate the net force needed to accelerate a 1000-kg car at ½ g. Solution: The car s acceleration is a = ½ g = ½(9.80m/s 2 ) 5.0m/s/s. We use Newton s second law to get the net force needed to achieve this acceleration. 2 F ma (1000 kg)(5m / s ) 5000 N

14 Ex2: Force to stop a car What net force is required to bring a 1500-kg car to rest from a speed of 100km/h within a distance of 55 m? Solution: We use Newton s second law, ΣF=ma, but first we must determine the acceleration, a, which we assume is constant. We assume the motion is along the +x axis. We are given the initial velocity v 0 = 100 km/h = 28 m/s, the final velocity v = 0, and the distance traveled x-x 0 = 55 m.

15 Force is exerted in the opposite direction of velocity which is what the negative sign tells. Carry it out From equation 2-10c, we have v 2 v 2 0 2a( x x0 So we can rearrange and solve for a we get: a v 2 2( x v x ) 0 (28m / 2(55m) s) 2 ) 7.1m / s 2 The net Force required is then F ma (1500 kg)( 7.1m / s 2 ) 1.1x10 4 N

16 Newton s Third Law of Motion In any interaction between objects, a force is exerted on an object by another object. Forces come in pairs. Newton s Third law of motion states whenever one object exerts a force on a second object, the second exerts an equal and opposite force on the first. Consider a hammer and a nail: The hammer exerts a force on the nail and at the same time the nail exerts an equal and opposite force on the hammer.

17 Newton s Third Law Sometimes this law is paraphrased as to every action there is an equal and opposite reaction. It is important to realize the action force and reaction force are acting on different objects.

18 Which force is which? Consider an ice skater. Since there is very little friction between the skates and the ice, she will move freely if a force is exerted on her. If she pushes on the railing, she moves backwards. Does her push on the railing cause this? Or is it the reaction force that causes her acceleration? Remember, an object accelerates in the direction of the net force acting on it

19 Your turn to Practice