Lecture 05: Free Body Diagrams

Physics 2210Fall Semester 2013

Announcements

● Schedule next few weeks:● 9/08 – Unit 3● 9/10 – Unit 4● 9/15 – Unit 5 (guest lecturer)● 9/17 – Unit 6 (guest lecturer)● 9/22 – Unit 7, Exam Review

● work practice exam in discussion● 9/24 – Exam 1, Units 1-6● 9/25 – Unit 7 HW due

Mechanics Lecture 5, Slide 3

Today's Topic: Free Body Diagrams

a) Stringsb) Springsc) Gravity

Suggested Problem Solving Template

Free-body diagrams areuseful in generating equations.

Mechanics Lecture 5, Slide 5

Mechanics Lecture 5, Slide 6

Mechanics Lecture 5, Slide 7

Example: Masses on Springs

Masses m1 = 5.0 kg and

m2 = 8.5 kg are

suspended by springs from the roof of an elevator as shown. The spring constant of both springs is 240 N/m. The elevator is moving downward, slowing down at 2.5 m/s2. What are the extensions of the springs from their unstretched lengths?

Example: Mass on a Ramp

The mass m = 13.0 kg is initially at rest on a frictionless ramp as shown. The angle = 22°. If the mass starts 5.0 m from the end of the ramp, how long will it take to reach the level floor?

Example: Mass on a Ramp, with Friction

The mass m = 13.0 kg is given an initial velocity of v

0 = 4.0 m/s down the

ramp, which now has friction on its surface. The mass slides 2.5 meters before coming to rest. The angle = 22°. What is the magnitude of the frictional force?

Example: Loop the Loop

A car of mass m = 400.0 kg is driving a “loop-the-loop” of radius 24.0 m at constant speed. What is the minimum speed required such that the car does not fall off the loop at the top position?

Example: Tetherball

A tetherball (see picture) with mass 1.0 kg rotates in a perfect circle with a period of 3.0 seconds. The length L of the (massless) cord connecting the ball to the pole is 2.5 m. What angle does the cord make with respect to the pole?

Example: Simple Gravitational Orbit

A space telescope of mass 10,000 kg is in a stable orbit above the Earth at an altitude h = 3,630 km. The radius and mass of the Earth are R

E = 6,370 km and

ME = 6.0x1024 kg, respectively.

Newton's gravitational constant is G=6.672x10-11 Nm2/kg2. (a) what is the acceleration of the space telescope? (b) if the telescope's mass were to increase, what would need to happen to its speed in order to maintain the same orbit?