Lecture 8
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1) Newton's third law states that for every action, there is an equal and opposite reaction. Whenever one object exerts a force on a second object, the second object exerts an equal force back on the first. 2) Momentum is defined as the product of an object's mass and velocity. It represents the difficulty of stopping or changing the motion of an object. Objects with greater mass or velocity have greater momentum. 3) The change in an object's momentum is called impulse. Impulse depends on both the magnitude of the force applied and the duration of its application. A longer application of force results in a greater change in momentum.
Lecture 8
- 1. Third Law For every action there is an equal and opposite reaction. Some action/reaction pairs: I push on the floor, the floor pushes back on me with equal force (unless it breaks). Tug of war (when at a standstill) – west group pulls rope with a force equal in size but opposite in direction to east group.
- 2. Simple Rule: Action: Object A exerts a force on object B Reaction: Object B exerts a force on object A A B F on A due to B F on B due to A
- 3. 3rd law example problem A 5 kg and a 1 kg mass collide. Which experiences the larger force? Explain.
- 4. Rolling How does a car accelerate? The wheels are turned by the motor. What would happen if there was no friction between road and tire? Wheel would spin but car wouldn’t accelerate. Friction between road and tire is also responsible for force that keeps car turning when changing direction. F of tire on road F of road on tire
- 6. Action/Reaction different masses What happens when A and B (equal mass) collide? Which one (if any) hits harder? Now, what if A and C collide where C is more massive than A? Which one hits harder? Action/Reaction forces are a pair – they are always and must always be the same size. A B C A
- 7. Cannon Action forces and reaction forces must be the same size. Why does the cannonball fly so fast? Why doesn’t the cannon move as much as the ball? Recall Newton’s 2nd law: acceleration = force/mass F m a = F m a =
- 8. Rockets If the rocket was in a vacuum would it still work? Yes – Rockets are a little like the cannon. (Demo)
- 9. Wrapping up Newton’s Laws An object will not accelerate (change direction or speed) unless acted upon by an unbalanced force. The acceleration of an object is proportional to the force on it and inversely proportional to mass (a = F/m). So what will happen to acceleration if you double force with same mass? If you double mass with same force? If object A exerts a force on object B then Object B exerts an equal in magnitude but oppositely directed force on A.
- 10. Momentum
- 11. What is momentum? Is it harder to stop something that is moving quickly or something that is moving slowly? Is it harder to stop something that has more mass or something that has less mass? How difficult something is to start or stop. More than just inertia (mass) includes how quickly something is already moving.
- 12. Momentum: Momentum = mass * velocity Momentum has a direction and that direction matches the direction of motion. Changing direction requires a change in momentum.
- 13. So objects with wildly different masses and velocities can have same momentum. V v
- 14. Example A motorcycle of mass 200-kg travels with a velocity of 50 m/s. What is its momentum? A car of mass 1000-kg travels with a velocity of 10 m/s. What is its momentum?
- 15. Changes in Momentum What causes a change in velocity? An acceleration, but what causes an acceleration? A Force: The greater the force and the longer it acts the greater the change in velocity. m v v m v m F
- 16. Impulse Impulse is the change in momentum. Consists of: Force (produces the velocity change) Time (how long the force was applied)
- 17. Impulse – Momentum: Impulse = change in momentum F*t = m2*v2 – m1*v1 OR F*t = Δmv
- 18. Coming to a stop: Braking: Low force over long time Crash: High force over short time. What is the momentum change for a truck braking to a stop? For a truck hitting a wall? Result is the same: same mass, same starting velocity and final velocity is zero. crunch! v F v v
- 19. Increasing Momentum Larger force applied over longer time will cause greatest increase. Rocket: tremendous force applied for several minutes to reach escape velocity. Rifles: why is a rifle long? Why wouldn’t you use a pistol to shoot something far away?
- 20. Rifles: Bang! (hot gasses push) Gasses escape... Gasses escape...
- 21. Decreasing Momentum Remember the truck: hitting a wall (fast stop) results in much more force than a controlled stop. Increasing the time a collision takes reduces the force experienced. Can you think of any examples? Airbags, crumple zones in cars. Boxers who dodge backward as they are hit. Bungee Jumping. Examples are endless.
- 22. Decreasing Momentum Slow change – by moving backward with the hit you decrease the force by increasing the contact time. Fast change – don’t move the wrong way, you increase the force by decreasing the contact time.
- 23. Demo: Fast vs. Slow changes 2 meter stick, 2 100 gram weights. Weight 1 attached 90 cm from table Weight 2 attached 10 cm from table Both by thin threads. What will happen when each is dropped (from the same height)?
- 24. Bouncing Which results in a greater impulse: bouncing stopping Look at momentum change: bounce: m(v2-v1) = m(v-(-v)) = 2mv stop: 0 – m*(-v) = mv v v 0 v boing!
- 25. Demo: Happy and Sad balls. One ball does not bounce. Other ball will. Which imparts more impulse? Why?
- 26. Conservation of Momentum Momentum is conserved. In a collision or other interaction, momentum is neither created nor destroyed. Recall the cannon example from Newton’s Third law. What was net momentum before cannon fired? What is net momentum (ball + cannon) after it is fired?
- 27. Momentum before = 0 Momentum after must be 0 (momentum is conserved). 0 = mc*vc + mb*vb So vc and vb will be in opposite directions to make the sum zero. Can we figure out what proportion their sizes will be?
- 28. Collisions Imagine two 1-kg carts. Momentum before = 1kg*10m/s = 10 kg*m/s momentum after must be equal. 2 kg * v = 10 kg*m/s v = 5 m/s
- 29. Wrapping up: Momentum is conserved (I know, I know, another conservation law – there are a few of them). Momentum is proportional to velocity and mass of the object. Impulse is a change in momentum. It is proportional to the force and the contact time.