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

PHYS 172: Modern Mechanics Summer 2012 Lecture 9 – Rate of Change of Momentum Read 5.1-5.7

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.

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

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

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

Curvilinear Motion

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

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

The Momentum Principle for components A 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

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 ?

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!

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!

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

Example: mass on spring, in motion mg 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

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?

No Lecture on Wednesday!! PHYS 172: Modern Mechanics No Lecture on Wednesday!! Lecture 9 – Rate of Change of Momentum Read 5.1-5.7