Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 16-18

F0m1

m2

Two blocks, on a frictionless table, have masses m1 and m2. They are connected by a massless, unstretchable string. If a force F0 is applied to the block m2, what is the tension in the connecting string?

Quiz

Quiz

1. If and find the dot product

jiA

43 jiB

32

2. For the two vectors shown below, find the dot product.

A

B

Charles KaoHong Kong

William BoyleBell Labs

The Nobel Prize in Physics 2009

Kao: "for groundbreaking achievements concerning the transmission of light in fibers for optical communication“

Boyle and Smith: "for the invention of an imaging semiconductor circuit – the CCD sensor"

George SmithBell Labs

• Stone Age

• Bronze Age

• Iron Age

• Ice Age

What is Information Age?

Information Age

The cost of the transmission, storage and processing of data has been decreasing extremely fast

Information is available anytime, any place, and for everyone

Information and knowledge became a capital asset

All of this became possible because of several revolutionary ideas

Laser and semiconductor laser

Transistor

Computer

World-Wide Web

Optical fibers

… Are invented by physicists

Integrated circuits

Telecommunications

How can we send light over long distances?

Air? Only within line of sight; High absorption and scattering, especially when it rains

Are there any “light wires” (optical waveguides)?

Copper wire? High absorption, narrow bandwidth 300 MHz

Glass? Window glass absorbs 90% of light after 1 m.Only 1% transmission after 2 meters.

Sand?!

Transmisson 95.5% of power after 1 km 1% of power after 100 km: need amplifiers and repeaters

Total bandwidth ~ 100,000 GHz!!

Ultra-low absorption in silica glasses

Silica (Silicon dioxide) is sand – the most abundant mineral on Earth

Predicted 1965 (Kao), in first low-loss fiber in 1970

Total internal reflection!

n1 > n2

How to trap light with transparent material??

Light coming from more refractive to less refractive medium experiences total reflection – get trapped there!

Examples of total internal reflection

Water: critical angle ~ 49o

Charge-coupled device

MOS capacitorPhotons generate charge which becomes trapped

The principle behind read-out of a CCD chip. One row at a time is shifted through an A/D converter which makes the output signal digital.

http://digitalimagingu.com/articles/microscopyimaging.html

http://digitalimagingu.com/articles/microscopyimaging.html

2 or 3 D motion

22

21

22

2

1

mVmVrdFW

r

r

net

rdFWL

Definition of work:

Kinetic energy: 2222

|| 2222zyx mVmVmVVm

Work-energy theorem:

A person carries a bag of groceries of mass M with a constant velocity at the same height from the ground. Find the work done by a person on a bag.

Problem 1 p. 122

A man pushes up on a 100 kg block with a force such that it drops from 2 meters to the ground at a constant velocity.

a)How much work is done by gravity?b)What is the magnitude of the force he exerts?

A person is pulling a crate of mass M along the floor with a constant force F over a distance d. The coefficient of friction is .

(a) Find the work done by the force F on the crate.(b) Same if F changes as F0(1+x2/d2). (c) Find the work done by the force of friction on the crate (F is constant). (d) Find the net work done on the crate if the crate is pulled with a constant

velocity. (e) Find the final velocity of the crate if the crate is pulled with a non-zero

acceleration starting from the rest.

M

Work Energy Theorem

22

222

1

initialfinalr

r

total

mVmVrdFW

22

2222

11

22

11

initialfinalyx

yx

totaly

yx

yx

totalx

mVmVdyFdxF

ixxkFLawsHooke

)(:' 0

x

positionunstrechedisx0

Problem 2 p.122

A 3 slug mass is attached to a spring which is pulled out one foot. The spring constant k is 100 pounds/ft. How fast will the mass be moving when the spring is returned to its unstretched length? (Assume no friction.)

Problems from handout

Problem 1

How many joules of energy does 100 watt light bulb use per hour? How fast would a 70-kg person have to run to have that amount of energy?

Problem 2

A car is stopped by a constant friction force that is independent of the car’s speed. By what factor is the stopping distance changed if the car’s initial speed is doubled?

Problem 3

A 5.00 kg block is moving at v0=6.00 m/s along a frictionless, horizontal surface toward a spring with constant k=500 N/m that is attached to a wall.

a) Find the maximum distance the spring will be compressed.

b)If the spring is to compress by no more than 0.150 m, what should be the maximum value of v0?

Quiz Ch 7 (a)

A block of mass m is attached to a spring, spring constant k, and is on a table with coefficient of friction . The spring is unstretched at x=0.

1. Find the work done by the spring and the work done by the table if the mass moves from A and B.

2. Find the work done by the spring and work done by the table if the mass moves from B to A.

3. Find the total work done by the spring for the round trip.4. Find the total work done by the table for the round trip.

mx=0 x=A x=B

A block of mass M is on a horizontal surface and is attached to a spring, spring constant k. If the spring is compressed an amount A and the block released from rest, how far will it go before stopping if the coefficient of friction between the block and the surface is ?

How will this answer change is the block is not attached to the spring??

Quiz Ch 7 (b)

Consider the spring force given by Fx = –kx+nx2 Consider = 0 (1 + x/d).

Quiz Ch7 (c)

y

A block of mass m slides down on the larger block of mass M (see the figure below). There is non-zero coefficient of friction between the two blocks. Neglect the friction between the block of mass M and the table.

1) Plot the free body diagram for each of the blocks;

2) Find the work done by gravity on the block of mass m (the smaller one) in two coordinate systems shown above, if the height of the inclined plane is H.

x x

y

Have a great day!

Reading: Chapter 8Hw: All Ch 7 problems and exercises