Review: Newton’s 1st & 2nd Laws 1st law (Galileo’s principle of inertia)- no force is needed to keep an object moving with constant velocity 2nd law (law of dynamics) – a force is needed to change the velocity (i.e., accelerate) of an object, how much: F(in N) = m(in kg)  a(in m/s2)

Acceleration due to gravity w = m  g F = m  g = m  a  a = g for any m weight, w

Problem -1 Two forces act on a 4 kg object. A 14 N force acts to the right and a 2 N force acts to the left. What is the acceleration of the object? Net force = 14 N  2 N = 12 N (to the right) F = m a  12 N = 4 kg x a  a = 3 m/s2  the object accelerates to the right at 3 m / s2. 14 N 2 N 4 kg

Problem 2 Push = 10 N Friction force = 2 N 2 kg A 2 kg box is pushed by a 10 N force while a 2 N friction force acts on the box. What is the acceleration of the box? Net force = 10 N – 2 N = 8 N to the right acceleration = Force / mass = 8N / 2 kg = 4 m/s2 to the right.  acceleration is in the direction of the NET Force

Net Force on system = total mass  a Problem: down the track (no friction): find the acceleration, a, of the blocks T M m M w = mg Net Force on system = total mass  a mg = (m + M) a  a=mg/ (m+M)  (m/M)g, if M is much bigger than m the force on m is applied to M through the string tension T

a = mg/ (m+M)  (m/M)g m= 20g m = 40g M (g) a (m/s2) 294 0.67 1.33 600 0.33 0.65 852 0.23 0.46 If Galileo had done this experiment, Newton’s Second Law would be Galileo’s Second Law

Newton’s third law (lecture 7) (deals with the interaction of 2 objects) For every action there is an equal and opposite reaction. We will discuss collisions, impulse, momentum and how airbags protect you in a crash

Newton’s 3rd Law If object A exerts a force on object B, then object B exerts an equal force on object A in the opposite direction. B A B  A A  B

Example What keeps the box on the table if gravity is pulling it down? The table exerts an equal and opposite force upward that balances the weight of the box If the table was flimsy or the box really heavy, it would fall!

The bouncing ball Why does the ball bounce? It exerts a downward force on ground the ground exerts an upward force on it that makes it bounce

You can move the earth! The earth exerts a force on you you exert an equal force on the earth The resulting accelerations are not the same Fon earth = - Fon you MEaE = myou ayou You have an influence on every object in the Universe!

Action/reaction forces always act on different objects A man tries to get the donkey to pull the cart but the donkey has the following argument: Why should I even try? No matter how hard I pull on the cart, the cart always pulls back with an equal force, so I can never move it.

Friction is essential to movement The tires push back on the road and the road pushes the tires forward. If the road is icy, the friction force between the tires and road is reduced.

You can’t walk without friction You push on backward on the ground and the ground pushes you forward.

Demonstrations Bouncy and non-bounce ball Dropping the beakers physics professor Bouncy and non-bounce ball Dropping the beakers Stunt man jumping off of a building

Impulse When two objects collide they exert forces on each other that last only a short time We call these short lasting, but usually strong forces IMPULSIVE forces. For example when I hit a nail with a hammer, I exert an impulsive force

What is impulse? If a force F acts for a time t, then the impulse is the Force  time = F  t Since force is measured in Newtons and time in seconds, impulse will be measured in Newton-seconds. IMPULSE = F  t

Momentum The term momentum is used quite often in everyday conversation about many things. For example, you may hear that one team has the momentum, or that a team has lost its momentum. Momentum is a physics term that has a very definite meaning. If an object has a mass m and moves with a velocity v, then its momentum is mass  velocity = m  v

Momentum = m  v In physics, if something has momentum, it doesn’t loose it easily and if it doesn’t have it, it doesn’t get it easily – something has to happen to an object to change its momentum Impulse can change momentum, in fact change in momentum = impulse If an object gets an impulse, F  t, then its momentum changes by exactly this amount

Knock the block over The bouncy side knocks the block over but not the non-bouncy side

Elastic and inelastic Collisions (bouncy) (non-bouncy) Which ball experiences the largest upward force when it hits the ground? Force on The ball Force on The ball

Bouncing ball The force that the ball exerts on the ground is equal to and in the opposite direction as the force of the ground on the ball. The ball that bounces back not only must be stopped, but must also be projected back up. The ground exerts more force on the ball that bounces than the ball that stops.

Physics explains it! Beakers dropped from same height so then have the same velocity (and momentum) when they get to the bottom. One falls on a hard surface The other falls on a cushion. hard soft

Why prevents the beaker that falls on the cushion from breaking? First, what causes anything to break? If an object experiences a large enough FORCE then it might break. Why does the beaker that falls on the cushion experience a smaller force? Both beakers have the SAME change in their momentum – they both hit the bottom with the same speed and both end up with zero velocity.

The beaker that shatters comes to rest more quickly than the one that gently slows down on the cushion  this is the key point! According to the impulse-momentum relation: Impulse = Force  time (F  t) = change in momentum F  t is the same for both. Since the one on the cushion takes longer to slow down the force on it is less, t is bigger F smaller

Air bags The same thing is true for airbags They protect you by allowing you to come to rest more slowly, then if you hit the steering wheel or the dash board. Since you come to rest more slowly, the force on you is less. You will hear that “airbags slow down the force.” this is not entirely accurate but it is one way of thinking about it.

Momentum and Collisions The concept of momentum is very useful when discussing how 2 objects interact. Suppose two objects are on a collision course. A B We know their masses and speeds before they hit The momentum concept helps us to see what can happen after they hit.

Conservation of Momentum One consequence of Newton’s 3rd law is that if we add the momentum of both objects before the collision it MUST be the same as the momentum of the two objects after the collision. This is what we mean by conservation: when something happens (like a collision) something doesn’t change – that is very useful to know because collisions can be very complicated!

Read more about it http://www.physicsclassroom.com/Class/momentum/U4L1c.html http://www.geocities.com/thesciencefiles/homerun/homerun.html http://www.k12.nf.ca/gc/Science/Physics3204/Projects2003/SlotA/ProjectA2/index1.htm