Review

1. Review Conversions, Motion, Motion Graphs, Freefall, Projectile Motion

2. Conversions • Use Dimensional Analysis • The Unit that you want should be on the top • The unit that you have should be on the bottom • Units that might be on the test • 109 nm=1 m 106μm=1m 10 6m= 1 Mm • King Henry Died Drinking Chocolate Milk • Kilo, Hecta, Deka, Base, Deci, Centi, Milli

3. Examples Convert 10 cm into km Convert 900 nm into meters

4. Motion Speed=distance/time (scalar) Velocity=displacement/time (vector) Example- Splat the cat runs on a circular track that is .25 meters. He completes a lap in 5 seconds. What is his speed? What is his velocity?

5. Motion Acceleration- The rate that velocity changes Measured in m/s2 If velocity is constant then a=0 Acceleration=ΔV/t or a=(Vf-Vi)/t Splat the cat started at rest and ran after a mouse in 2 seconds and he had an acceleration 5 m/s2. What was his final velocity?

6. UAM/FreeFall • Remember! If you have 3 motion variables you can solve for the other 2 • This is for constant acceleration only! • V f = V i+ at • Δx = V iΔt + ½ (a t2) • Vf2 = Vi2 + 2 a Δx • Δx = ½ (Vf + Vi) Δt • Δx=distance or displacement, Vf= final velocity, Vi= initial velocity • a=acceleration, t=time

7. Example Splat the cat was on top of a car, which had a constant acceleration of 10 m/s2 and he fell off the car after 5 seconds. How far did the car move before dropping dropping Splat?

8. FreeFall When objects are in freefall, the only force acting on the object is gravity, meaning there is no air resistance (in a vacuum) ALL objects will fall at a rate of 9.8 m/s2 Mass has no impact on acceleration due to gravity (g) When an object is falling make a(g) negative, Δx negative, and V negative When an object is moving up, make a(g) negative, Δx positive, and V positive

9. Example Splat the cat was dropped from a 50 meter tall building. (poor cat) How long did it take for Splat the cat to go Splat? Acceleration is negative here, is Splat slowing down??

10. Projectile Motion When an object is moving in two directions it is considered a projectile (bullet, something being thrown or kicked off a building) The x component and the y component do affect each other The y direction has acceleration (9.8 m/s2)- Use UAM equations There is no a in the x direction- Use V=d/t ONLY Time can be used in both directions

11. Example Splat the cat was taken to the top of a 50 m building and kicked off the building with a velocity of 10 m/s. How long does it take for Splat the cat to go splat? How far from the building does he land?

12. Graph Basics Slope=Δy/Δx, so look at the type of graph to determine what the slope equals Linear= constant slope Horizontal Line means m=0 Parabola means something is squared S-Shaped, something is cubed Inverse- Indirectly proportional

13. Motion Graphs On a D-T graph Slope=Velocity, + or – tells you the direction If Linear=constant velocity, no acceleration On a V-T graph Slope=acceleration, + or – tells you if you are speeding up or not Horizontal line or m=0 means no acceleration! On an A-T graph Straight Line=Constant acceleration If it is below or above the axis, it will tell you if your object is speeding up or slowing down

14. Example

15. Example

16. Review Forces, Circular Motion

17. Forces • Newton’s Laws • 1st Law • A body at rest stays at rest (and motion) until a force acts on it • Basically…Inertia • Inertia resists changes in motion (more mass=more inertia) • 2nd Law • F=ma • 3rd Law • For every force there is an equal and opposite force • Reaction- Action Pairs

18. Net Force When solving for acceleration of an object, you must use the net force When an object is in equilibrium the net force=0, so a=0 Happens when there is a constant velocity or the object is not moving Opposing forces are equal to each other when there is no net force

19. Types of Forces Weight Normal Force Force Applied Force of Tension Force of Friction

20. Weight You get weight by multiplying mass to 9.8 m/s2 What is the weight of 40 kg object? What is the force applied on a backpack that is being moved up at a constant velocity that has a mass of 10 kg?

21. Force of Friction The force that opposes sliding motion along a surface Ff=μFn The normal force is equal to the weight (Fg) of an object Static friction=not moving Kinetic Friction= moving, smaller

22. Example Solve for the coefficient of friction when an object is moving along a surface with a constant velocity that has a weight of 50 kg and the applied force is 50 N.

23. Force of Gravity There is an attractive force between two objects that have mass Fg= Gm1m2 r2 G=6.67 x 10-11 N(m/kg)2 What is the force of gravity between splat the cat (1 kg) and a person that is 50 kg when they are 1 meter apart? If the force of gravity is originally 10N, what happens when the distance is halved?

24. Centripetal Force • If an object is moving in a circle and you need to find the velocity or acceleration • Vt=(2πr)/T • Ac=(Vt)2/r • Centripetal force is not a different force • Fc=mac • Friction, gravity and tension are centripetal forces when moving in a circle • Always directed towards the center

25. Review Momentum

26. Momentum The quantity of motion Vector Measured in kg*m/s P=mv Change in momentum (stops, changes direction or speed) Δp=mΔV Or Δp=m(Vf-Vi)

27. Momentum-Impulse A force can cause a change in the object’s momentum FΔt=mΔV More time means the change in velocity can be greater More time can also mean that less force is needed to change the momentum What force is required to stop splat the cat (1 kg) from falling off a building when his velocity is 40 m/s in 1 second?

28. Conservation of Momentum • When no external forces then momentum is conserved • pi=pf • m1V1i + m2V2i = m1v1f + m2V2f • Collisions can be elastic or inelastic • Elastic • Objects break apart, kinetic energy is conserved • Inelastic • Objects stick together…So there is one mass and one final velocity • m1V1i + m2V2i = (m1 + m2)Vf

29. Example A 0.105-kg hockey puck moving at 48 m/s is caughtby a 75-kg goalieatrest. Iftheiceisfrictionless, atwhatvelocity will thegoalieslide on theice after catchingthepuck?

30. Review Work, Energy, and Power

31. Energy and Work Energy- the ability to do work Work- a change in energy Work- can convert energy into other forms Measured in Joules (kg*m2/s2 or N*m)

32. Work W=fd Distance must be parallel to the force If there is no distance, no work is done

33. Nonconservative Versus Conservative Nonconservative forces- forces that do not conserve energy (friction) Conservative forces- do conserve energy (gravity) Work done against conservative forces are not dependent on the pathway taken Ramp example

34. Mechanical Energy ME= KE + PE KE=1/2mv2 GPE=mgh Must be measured with respect to a reference point What is the GPE of splat the cat (1kg) if he is lifted to 10 meters off the ground?

35. Conservation of Energy Total energy is always conserved ME is not always conserved (friction) Pei + Kei =Pef + Kef mghi + ½ mv2i = mghf + ½ mv2f

36. Example Splat the cat (1 kg) is dropped from a 10 meter tall building, what is his velocity right before he goes splat? His kinetic energy?

37. Power P=W/t or P=ΔE/t P=FV Measured in J/s or Watts Power is the rate work is done