Physics 218: Mechanics Instructor: Dr. Tatiana Erukhimova

Lectures 16, 17, 18

F

Find F necessary to drag the box 1 at constant speed.

1

2

Friction everywhere.

The advantage of a pulley

What minimum force F is needed to lift the piano of mass M?

WORK (Chapter 7)

2 or 3 D motion

22

21

22

2

1

mVmVrdFWr

rnet

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 block of mass m starts at the top of an inclined plane. The coefficient of friction between the plane and the block is . Assuming the block slides down the plane calculate the work done by each force.

Work Energy Theorem

22

2222

11

22

11

initialfinalyx

yx

totaly

yx

yx

totalx

mVmVdyFdxF

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

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.)

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 Ch7

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 7Hw: Chapter 7 problems and exercises