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Physics 218
Lecture 10: From
Work to Energy
Alexei Safonov
Other tricks
• What is minimum velocity for the car
not to fall down?
– Radius, mass are given
– Key question: what tells you that the car
may not make it through the top point?
• Normal force!
• How about a problem with a ball on a
string that you rotate in vertical plane
with constant speed and you want it to
swing without sagging at the top?
–
What force should you look at instead?
• What if it is a bucket with a rock in it
and you don’t want it to fall on you?
– What force?
Conical Pendulum
A small ball of mass m
is suspended by a
cord of length L and
revolves in a circle
with a radius given
by r = LsinQ.
1. What is the velocity
of the ball?
2. Tension FT?
3. Calculate the period
of the ball.
Overview: Chapters 6 & 7
• Combine Chapter 6 & 7 into
three and one third lectures
Today we’ll cover Work:
• Intuitive understanding
• The math and multiple ways
to calculate work
Work
• The word “Work” means something
specific in Physics (~ like Force)
• The amount of Work we do is the
amount of Forcing we do over some
distance
• Example: If we are accelerating a car
for 1 mile, then there is a force and a
distance
– We do Work
Calculating the work
• Work is done only if the force (or
some component of it) is in the same
(or opposite) direction as the
displacement
• Work is the force done Parallel to
the displacement
– Think of it as “amount of displacement
should be affected by the force if it is doing
any work”
• Pushing a car to speed it up or to slow it down
Work for Constant Forces
• The Math: Work can be
complicated. Start with a simple
case. For constant forces, the
work is …(more on this later)
.
W=F d
1 Dimension Example
• Pull a box with a constant force of
30N for 50m where the force and
the displacement are in the same
direction
• How much work is done on the
box?
• W = F.d = 30N . 50m= 1500 N . m
= 1500 Joules
SP Checkpoint
• A box sits on the horizontal bed of a truck accelerating to the
left as shown. Static friction between the box and the truck
keeps the box from sliding around as the truck drives.
• The work done on the box by the static frictional force
as the accelerating truck moves a distance D to the left
is?
A.
B.
C.
D.
Positive
Zero
Negative
Depends on the speed of the truck.
SP Checkpoint
• A box sits on the horizontal bed of a truck accelerating to the
left as shown. Static friction between the box and the truck
keeps the box from sliding around as the truck drives.
• The work done on the box by the static frictional force
as the accelerating truck moves a distance D to the left
is?
A.
B.
C.
D.
Positive
Zero
Negative
Depends on the speed of the truck.
Work done and Work
experienced
• Something subtle: The amount of work
YOU do on a body may not be the same
as the work done ON a body
• Only the NET force on the object is used in
the total work calculation
– Add up all forces to get net force, calculate
work done on the object
• … Or add up the work done on an object
by each force to find the total work done!
– But be careful with signs!
Examples
• While you are lifting up a bottle with mass m, the
bottle moves a distance d with constant velocity.
As you lift it:
–
–
–
–
What is the force you exert?
What is the work done by you?
What is the work done by gravity?
What is the net work?
• You push a box with Force F on a rough floor with
coefficient of friction m for a distance d, and the
box moves with constant velocity. As it moves:
– What is the work done by you?
– What is the work done by friction?
– What is the net work?
You take a box of mass m and move it
(with ~zero constant velocity) to height h
and then lower it back (also with ~zero
velocity). As it moves, we calculate the
work done on it. The total work done on
the object is …
A.
B.
C.
D.
mgh at the top point, 2mgh when returns to the
lower point again
mgh at the top, but zero when at lower point
again
Zero at the top and zero at the lower point again
2mgh at the top, 4mgh by the time it returns to
lower point
SP Checkpoint
•
•
Three objects having the same mass begin at the same height, and all move
down the same vertical distance H. One falls straight down, one slides down a
frictionless inclined plane, and one swings on the end of of a string.
In which case does the object have the biggest total work done on it by all
forces during its motion?
A.
B.
C.
D.
Free Fall
Incline
String
Same
SP Checkpoint
•
•
Three objects having the same mass begin at the same height, and all move
down the same vertical distance H. One falls straight down, one slides down a
frictionless inclined plane, and one swings on the end of of a string.
In which case does the object have the biggest total work done on it by all
forces during its motion?
A.
B.
C.
D.
Free Fall
Incline
String
Same
2 Dim: Force Parallel to
Displacement
W = F||d = F.d = Fdcosq where q is the angle
between the net Force and the net displacement. You
can think of this as the force component in the
direction of the displacement.
Force
Force
Rotate
Displacement
F|| = Fcosq
Displacement
Examples
• Holding a bag of groceries in place
– Is it heavy?
– Will you get tired holding it?
– Are you doing “Work?”
• Moving a bag of groceries with
constant speed across a room
– Is it heavy?
– Will you get tired doing it?
– Are you doing “Work?”
• Lifting a bag of groceries a height h
with constant speed?
– Work by you?
– Work on the bag?
Groceries: With the math
• Holding a bag of groceries
– Work by you on bag: W=Fdcosq =(mg)*(0)*cosq = 0
– Work on bag W=Fdcosq =(0)*(0)*cosq = 0
• Moving a bag of groceries with constant speed
across a room
– Force exerted by you = mg, Net Force on bag = 0
– Work on bag= F.d = Fdcosq =0*dcosq =0
– Work exerted by you =Fdcosq =mgd*cos(900)=0
• Lifting a bag of groceries a height h with
constant speed?
– Work on bag = Fd*cosq = (0)*h*(00) = 0
– Work by you =Fdcosq =(mg)hcos(00)=mgh
Work in Two Dimensions
• You pull a crate of mass M a distance X along a
horizontal floor with a constant force. Your pull has
magnitude FP, and acts at an angle of Q. The floor
is rough and has coefficient of friction m. Determine:
• The work done by each force
• The net work on the crate
Q
X