1. Exam 1 Wednesday, June 27 8:00-9:30pm In this room
Covers Chapters 1 through 5.
Bring a calculator and #2 Pencils

2. PHYS 172: Modern Mechanics Summer 2012
Lecture 9 – Rate of Change of Momentum Read

3. Rules for Identifying Forces on a System
Choose a system.
Show all forces due to objects in the surroundings that interact at a distance with the system. Label each force with the name of the interacting object.
Show all forces due to objects in the surroundings that are touching the system. Label each force with the name of the object.

4. Example – Hanging Ball System: Ball Surroundings: Earth, Wire
Free-body diagram

5. Q4.10.a: What objects exert significant forces on the red block?
A) Earth, String 1, String 2
B) Earth, String 1, String 2, Hand
C) Earth, String 1, String 2, Hand,
Ceiling
D) Earth, Hand, Ceiling

6. Equilibrium with two strings
Know mass.
Need to know the force F2 required to achieve 
Static equilibrium y m
Break into x and y components x

7. Curvilinear Motion

8. Changing momentum: curving motion
Parallel component
(Along trajectory)
Rate of change of direction
Perpendicular component
(to trajectory)
Remind – p is a function of time, and both |p| and p^ may also depend on time.
Direction of motion in point A A

9. Rate of change of direction
Length of path A = vt
Similar angles
Angle =
For small angle:
Direction:
For small angles is
perpendicular to
is directed toward the
center of the circle
- Normal to the path toward center of the “kissing” circle

10. The Momentum Principle for componentsA
Direction of motion in point A
Parallel component:
Perpendicular component:
Discuss briefly:
The magnitude is changed only if there is a force component along path
The direction is changed only if there is force component perpendicular to path
Rate of change of magnitude p Rate of change of direction of p

11. Example: the Moon and the Earth
Mass of the Moon: mM = 7×1022 kg
Distance from the Earth: R = 4×108 m
Period: T = 28 days
Question: = ? R
Solution: mM
Parallel: =0
Perpendicular:
What is the direction of ?

12. Example: the Moon and the Earth
Mass of the Moon: mm = 7×1022 kg
Distance from the Earth: R = 4×108 m
Period: T = 28 days
Mass of the Earth: mE = 6×1024 kg
Question: FEarth on M=? R mE mM
Solution:
From motion path:
Discuss the fact that following motion we can determine dp/dt, and if we know dp/dt we know that there was interaction and we can deduce what was the force. However, nature of the interaction (force) does not matter. And vice versa – if we know force we can predict motion.
any force
motion of any object
This is precise – works at any speed!

13. Clicker 5: Turning car A D B C
What is the direction of the net force acting on people in the car? B C
Right turn – are you “thrown to the left”? What is the direction of the force?
You are moving in a straight line – to change your trajectory the force must be applied, it is the door which pushes you and keeps you moving along curve!

14. Clicker: Ferris wheel Assume constant What forces act on a person?
gravity
seat
6. Is the gravitational force constant?
Yes No
7. Is the net force |Fnet| constant?
Yes No
8. Is |Fseat| constant?
Yes No

15. Example: mass on spring, in motionmg mg
Same approach can be used – refer to example. Will talk about this kind of motion later.
Note: this problem can be solved using iteration, but it also has analytical solution (address later) mg
Force on mass due to spring changes as |s| changes . 16

16. Clicker: Rate of change of momentum
Highest point
Equilibrium
Lowest point
2. What is at the equilibrium point?
3. What is at the lowest point?
4. What is at the highest point?

17. No Lecture on Wednesday!!
PHYS 172: Modern Mechanics
No Lecture on Wednesday!!
Lecture 9 – Rate of Change of Momentum Read