Week 6 Assignments: - HW #5 Chp 4: Q11, Q22, P9, P33, P83 || Q17, Q21 P13, P55, P82

- MasteringPhysics: - Assignment #5

Week 6 Reading: Chapter 1-5 - Giancoli

This Week’s Announcements:

Lecture 11: Newton’s 3rd Law

Due: 9/29

* HW #4 due today

* Midterm I will be as scheduled (on tuesday 9/29)

* Midterm class period (09/29) is the last day to turn in late HW# 1 - 4

- 20 questions (~10 MC-TF-SA / 10 Word problems)

* Midterm I is tuesday 09/29:

- one 3x5” card (one side) of notes

- I posted a copy of an old midterm (without solutions) to give an example (just studying it will be not be enough to do well)

- no problems will directly require calculus, but vectors will be required

- Material to be tested: - Chp 1 - Chp 2 --- 2.2-2.7 - Chp 3 --- 3.1-3.4; 3.5-3.9 - Chp 4 --- all - Chp 5.1-5.4 --- all

-all clicker Qs; and any examples worked in class

* Midterm class period (09/29) is the last day to turn in late HW# 1 - 4

- no smart devices (even for listening to music)

- arrive early so that seating arrangements can be worked and still provide you most of the time

- If you need OCD accommodations make sure to get them arranged with me (privately) before the exam

α mg

N

You are dragging luggage up a ramp (making an angle α with the horizontal). There is friction between you and the ramp, with a rather large coefficient of kinetic friction, µk = 1. The luggage is heavy (as usual you’ve over-packed), and you wish to exert the least amount of force pulling the luggage (Fp). What is the optimum direction, θ, in which to pull the luggage such that it moves up the ramp at a constant speed with the least amount of effort (force)?

θ Fk

Fp

α

4)

a) Straight up (θ = 90 – α)

b) Along ramp (θ = 0)

c) Somewhere in between

Clicker Question:

T1 T2

Fg

T1 sinθ1 T1 cosθ1 T2 cosθ2

T2 sinθ2 θ2 θ1

X: Y: -T1cosθ1 + T2cosθ2 = 0 T1sinθ1 + T2sinθ2 = mg

T2

T1

Fg

Fnet = 0

- Mass isn’t accelerating

Vector Forces

- Equilibrium

Clicker Question:

6)

a) yes

You are in the process of designing a suspension bridge. At one junction six cables intersect and you measure the tension forces (direction and magnitude) listed. Assuming that you wish your bridge junction to remain at rest for a long while, should you be satisfied with the following cable tensions.

b) no 10 kN 10 kN

20 kN 20 kN

50 kN

80 kN

30o 30o

Clicker Question:

5)

a) Each 4.9 N upward

What is each piece of the string’s tension, T, caused by the 1 kg mass if we now have replace the joint with a pulley? Assume the strings are vertical.

T

mg

b) Each 4.9 N downward

c) Each 9.8 N upward

d) Each 9.8 N downward

e) Tension on the left string is 9.8 N upward and the tension in the right string is 9.8 N downward

Clicker Question:

5)

a) Each 4.9 N upward

T

mg

b) Each 4.9 N downward

c) Each 9.8 N upward

d) Each 9.8 N downward

e) Tension on the left string is 9.8 N upward and the tension in the right string is 9.8 N downward

What is each piece of the string’s tension, T, caused by the 1 kg mass if we now have replace the joint with a pulley? Assume the strings are vertical.

Roads designed for high-speed travel are banked to give the normal force a component towards the center of the curve. A properly designed bank will permit a car to go around a circular curve without any need for frictional forces (steering). ---- same reason applies for why airplanes bank when they turn.

What angle should a road with a 300 m radius of curvature be banked for travel at 30 m/s?

Centripetal Force

X:

Y:

N sin θ = Fnet = mv2/r

N cos θ = mg Fnet = mv2/r = (mg/cos θ) sin θ

v2/r = g tan(θ)

θ

N

mg

Fnet

θ

r

Clicker Question:

7) Now lets consider what happens if we rely on friction rather than banking. Lets say Jimmy Johnson enters a turn of 250 m (~0.15 mil) radius of curvature, at 70 m/s (155 mph). If we assume a NASCAR car (+ driver) has a mass of 1500 kg and a µs of 1.0 will the car be able to track the curve without wiping out in a massive crash?

b) no

a) yes

Clicker Question:

7)

b) no

a) yes

Now lets consider what happens if we rely on friction rather than banking. Lets say Jimmy Johnson enters a turn of 250 m (~0.15 mil) radius of curvature, at 70 m/s (155 mph). If we assume a NASCAR car (+ driver) has a mass of 1500 kg and a µs of 1.0 will the car be able to track the curve without wiping out in a massive crash?

Newton’s 3rd Law

For a force there is always an equal and opposite reaction: or the forces of two bodies on each other are always equal and are directed in opposite directions.

-Newton

- forces between two objects always come in pairs

- forces equal in magnitude

- directed in opposite directions

- forces act of different objects Fr-f

Ff-r

Newton’s 3rd Law: Examples

Hero of Alexandria: Circa: time of Christ - Invented first

steam engine:

- Invented syringe - Invented forerunner of motion picture - Invented the vending machine

Action

reaction

- First known use of wind power to power an instrument - Many others

Newton’s 3rd Law

a⊕ = Fdown/m⊕ ame = Fup/mme

- Newton’s 3rd law: Fup = -Fdown

mme = 100 kg

m⊕ = 6.0 x 1024 kg