Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 15-17

Block 1, of mass m1, is placed at rest on an inclined plane. It is attached by a massless, unstretchable string to block 2, of mass m2. The pulley is massless and frictionless and just changes the direction of the tension in the string. Assume the variables are such that m1 slides down the plane, starting at t=0. The coefficient of friction between the plane and m1 is the constant .

2

1

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

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:

Work Energy Theorem

22

222

1

initialfinalr

r

total

mVmVrdFW

22

2222

11

22

11

initialfinalyx

yx

totaly

yx

yx

totalx

mVmVdyFdxF

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?

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 if the mass moves from A and B.

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

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)

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