Transcript Mechanics Instructor: Dr. Tatiana Erukhimova Lectures 16, 17, 18

Physics 218: Mechanics
Instructor: Dr. Tatiana Erukhimova
Lectures 16, 17, 18
Friction everywhere.
2
F
1
Find F necessary to drag the box 1 at constant speed.
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
Definition of work:
 
W   F dr
L
Kinetic energy:
 2
2
2
2
mV
mVx
m |V |
mVz
y



2
2
2
2

r2
Work-energy theorem:
2
2

 mV2 mV1
W   Fnet  dr 


2
2
r1
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
x2 y 2
F

total
x
x1 y1
dx 
x2 y 2
F

total
y
x1 y1
dy 
mV
2
final
2
2
initial
mV

2
M
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.


Hooke' s Law : F  k ( x  x0 )i
x0 is unstreched position
x
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
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;
y
y
x

x
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.
A
bt 2
2m
B 0
C
bt 2
- m gt
- m gt + Const
2m
✔D none of the above
Have a great day!
Reading: Chapter 7
Hw: Chapter 7 problems and
exercises