1. Forces, Momentum, & Gravity
(Chapter 3)

2. Student Learning Objectives
Compare and contrast types of motion, laws of motion, and gravitational effects
Recall and apply each of Newton’s Laws
Relate momentum to impact force
Use conservation of momentum to analyze motion
Describe gravity and its effects

3. What is a force & when are forces balanced?
Forces can cause a change in motion; a net force results in acceleration. 
An object in mechanical equilibrium maintains its motion. There is no change.
Fnet = ∑ F

4. Practice
1) If a car engine provides 700 Newtons of push, and there is 200 Newtons of opposing friction, what is the net force on the car? Is this car in mechanical equilibrium? 2) If a car engine continues to provide 700 Newtons of push, but the friction force is increased to 700 Newtons, what is the net force on the car? Is this car in mechanical equilibrium? Would this cause the car to stop?

5. More Practice
3) Is a car with a constant velocity of 30 mph in mechanical equilibrium? Why must you keep pressure on the accelerator? 4) A 150 lb person is standing still on the floor. What is the net force?

6. What are Newton’s Laws of Motion?
Newton’s 1st Law of Motion
An object will remain at rest or maintain a constant velocity unless an unbalanced force causes the object’s motion to change. (Inertia)
Inertia is the tendency of an object to maintain its motion.

8. F = ma Newton’s 2nd Law of Motion
An unbalanced force acting on a mass gives the mass an acceleration in the same direction as the unbalanced force. (F = ma)
More push = more acceleration
F = ma

10. Sliding friction Normal Force
Sliding friction is in the opposite direction from the motion.
Normal force is perpendicular to the surface.
Support Force FN
Big
Box
Motion Ff

11. Practice
1) If the force on a 5 kg mass is tripled, what will happen to the rate of acceleration? 2) A 2000 kg car engine provides 9800 N, southward, with an opposing frictional force of 1200 N. What is the average acceleration? 3) Is there a normal force acting on you now? In what direction(s)?

12. Mass vs Weight Mass is a fundamental quantity.
Mass is the amount of material contained in an object.
Empty 747 Jet
160,000 kg
Average Man
73 kg
5¢ coin kg
Earth
5.972 x 1024 kg

13. W = mg Weight is the gravitational force acting on a mass. Earth
1kg = 2.2 lbs = 9.8 N
W = mg

14. Mass vs Inertia Inertia depends on mass. More mass  More inertia
 Harder to change motion

15. Practice
1) Mass is often defined in elementary school as “the amount of space an object takes up”. Why is this not correct?
2) Does weight depend on volume?
3) If you were instantly transported to Mars, would you change:
Mass? Weight? Inertia?

16. Math Practice 4) A person weighs 150 lb (667 N) on Earth.
What is the mass of this person?
What would the person weigh on Mars where the acceleration due to gravity is 3.72 m/s2?

17. Vectors Vectors add size and direction.

18. Practice
An airplane’s speedometer reads 500 mph North. What is the net velocity of the airplane relative to the ground:
Wind is blowing North at 50 mph?
Wind is blowing South at 50 mph?
Wind is blowing East at 50 mph?

19. F1 = −F2 Newton’s 3rd Law of Motion
When two objects interact, they create equal and opposite forces on each other. (Action-Reaction)
F1 = −F2
Same Pull
Opposite Directions

21. Space X

22. Practice
If I give the chair a good push, it goes from rest to having a velocity, and then stops. How do each of Newton’s laws apply to this system?
If a person weighs 135 pounds, how much force does the floor apply to the person? How much force does the floor apply to a person who weighs 175 pounds, if they stand on the same spot?

23. What is momentum?
Linear momentum is the combination of mass (inertia) and velocity.
The greater the momentum, the harder it is to stop an object!
p = mv

24. Practice
1) What is an example of a moving object that could have a large momentum because it has a large mass? 2) What is an example of a small object that could have a large momentum because it has a large velocity?

25. More Practice 3) Which has the most momentum?
10,000 lb (4535 kg) 18-wheeler parked at the curb
300 lb (136 kg) football player running 10 mph (4.46 m/s)
150 lb (68 kg) sprinter running 22 mph (9.83 m/s)
1200 kg car moving at 1 m/s

26. Angular Momentum L = mvr L v
Angular momentum is momentum in a circular path. L v
L = mvr

28. How does momentum affect the force of impact?
During an impact, the force of impact depends on how quickly the momentum is changed.
F = Dp t

31. Practice
What are some features of car design that decrease force of impact?
You (75 kg) are riding in your 2000 kg car at 67 mph (30 m/s) when suddenly a squirrel runs in front of you; you swerve, and hit a tree. If the duration of the impact is 1/2 of a second, what is the impact force?

32. How is conservation of momentum applied?
The total momentum of an isolated system is conserved.
Collisions
Elastic - separate
Inelastic - stick together
pf = pi
Lf = Li
m ↓ v ↑
r ↓ v ↑

33. Practice
1)Two cars of equal mass collide. One is traveling West at 30 m/s, the other is at rest. Then there is an inelastic collision between the two cars. If linear momentum is conserved, what happens to velocity? 2) An ice skater spins 7 m/s with outstretched arms. The radius of the circular path traced by her arms is 1 meter. Then she pulls her arms in, changing the radius of the circular path to 1/3 m. If angular momentum is conserved, what is her new spinning speed?

35. What is Newton’s description of gravity?
Newton’s Universal Law of Gravitation
Every object with mass attracts every other object with mass, with a force that depends directly on the masses of the two objects and decreases with the distance squared.
Fg = GMm d2

36. Mutual Force of Attraction
Both masses pull the same on each other!

37. Inverse Square Law
Force decreases with the square of the distance.

38. Practice
1) Would the acceleration due to gravity (9.81 m/s2) be different for an object dropped from a high mountain top than it is at sea level? 2) If Earth had twice as much mass, would this change your weight? Would it change your mass? 3) How would the gravitational force change if the distance doubled? Tripled?

39. More Practice
4) What is the gravitational attraction between Earth and a 75 kg person at sea level? What do we normally call this? (ME = 6 x 1024 kg, rE = 6.4 x 106 m) 5) Is the gravitational force zero in space?

40. What is Einstein’s description of Gravity?

41. According to Einstein More Mass = More Curvature
Einstein’s Theory of gravity
Every object with mass creates a curvature of space-time.
Mass does not create a force
Mass changes space
Space alters path of objects and light
More Mass = More Curvature

42. Image Credit: oneminuteastronomer.com

43. Question to Consider
What does gravity effect or cause? Name as many phenomena as you can.
How do Newton’s and Einstein’s descriptions of gravity compare and contrast?

44. Ocean Tides

45. Changing Systems Our Earth-Moon system is changing.
Earth’s rotation is slowing ( seconds/century)
Our Moon is drifting away (3.8 cm/year)
The synchronous orbit of the Moon (same face)

46. Weightlessness
The feeling of weightlessness occurs when an object and its reference frame accelerate at the same rate.
If there is no support force, then objects will fall together.

48. Practice The Sun's tidal affects are weak compared to the Moon. Why?
The astronauts on the space station have no weight. (true or false)
Does the moon have weight?