Phys101 Lecture 7,8 Circular Motion, Gravity, Summaries of Dynamics

Download Phys101 Lecture 7,8 Circular Motion, Gravity and more Summaries Dynamics in PDF only on Docsity!

Page 1

Phys101 Lecture 7,

Circular Motion, Gravity

Key points:

• Centripetal acceleration
• Uniform Circular Motion – dynamics
• Gravity

Ref: 5-1,2,3,5,6,7,8.

Highway Curves: Banked and Unbanked

When a car goes around a curve, there must be a net force toward the center of the circle of which the curve is an arc. If the road is flat, that force is supplied by friction.

Page 2

Highway Curves: Banked and Unbanked

Banking the curve can help keep cars from skidding. When the curve is banked, the centripetal force can be supplied by the horizontal component of the normal force. In fact, for every banked curve, there is one speed at which the entire centripetal force is supplied by the horizontal component of the normal force, and no friction is required.

Page 4

Example: Banking angle. (a) For a car traveling with speed v around a curve of radius r , determine a formula for the angle at which a road should be banked so that no friction is required. (b) What is this angle for an expressway off-ramp curve of radius 50 m at a design speed of 50 km/h?

Page 5

22  50

1389

(b) R 50m, 50 1389

0

(a)

1 2 1 2

2

2

  

  



 



  g tan. Rg tan v

v km/ h. m/ s

Rg tan v

F cos mg

R F sin mv N

N









(A) car’s engine is not strong enough to keep the car from being pushed out (B) friction between tires and road is not strong enough to keep car in a circle (C) car is too heavy to make the turn (D) none of the above

You drive your

dad’s car too

fast around a

curve and the

car starts to

skid. What is

the correct

description of

this situation?

I-clicker question 7-2 Around the Curve III

i-clicker question 7-3. Ball and String A) T 2 = 1/4 T 1 B) T 2 = 1/2 T 1 C) T 2 = T 1 D) T 2 = 2 T 1 E) T 2 = 4 T 1

Two equal-mass rocks tied to strings are whirled in horizontal circles. The radius of circle 2 is twice that of circle 1. If the period of motion is the same for both rocks, what is the tension in cord 2 compared to cord 1?

Newton’s Universal Gravitation

In vector form:

Direction: attractive

Gravity Near the Earth’s Surface

On the surface of the Earth, an object with mass m experiences the gravitational force due to the earth

2 2

2

g G MR 9_._ 80 m/ s

G MR m mg

E

E

E

E