Download work, energy, and simple machines

WORK, ENERGY, AND SIMPLE MACHINES
Work - the product of the force exerted on an object
and the distance the object moves in the direction
of the force.
W = F d cos θ
W: work
F: magnitude of force
d: magnitude of displacement
Units are Joules (J = Nm)
If a 1 N force moves an object 1 m, 1 Joule of work is
done.
Work is only done on an object if the object moves.
Work is only done on an object when the force and
displacement are in the same direction.
Example. Holding an object at the same height for
hours - you may get tired but you are doing no work on
the object. Even if you are moving and the object
remains at the same height, no work is being done.
What is the effect of doing work?
In simple terms, the work done on an object is equal to
the energy of motion or kinetic energy.
W  Fd cos  Ek  12 mv 2
What about the time it takes to move an object?
Power is the rate of doing work.
Power is the rate at which energy is transferred.
W
P
t
Units: Watts (W)
If you have a F vs d graph,
F (N)
d (m)
the area under the curve represents work.
Remember, work is done if a force is exerted in the
direction of motion.
If you are pushing or pulling something at an angle, only
the component that acts in the direction of motion is
doing work.
W = F d cos Θ
Example. Lawn mower. A person is doing work on the
lawn mower. The lawn exerts a force (friction) on the
lawn mower. W = Ffriction d cos Θ
Ex. 1 An applied force of 20. N accelerates a block
across a level, frictionless surface from rest to a
velocity of 8.0 m/s in a time of 2.5 s. Calculate the
work done by this force.
Ex. 2 Calculate the work done in lifting a 12 kg crate
from the floor to a platform 3.0 m above floor level at
a constant velocity.
Ex. 3 A truck pushes a car by exerting a horizontal
force of 500. N on it. A frictional force of 300. N
opposes the car’s motion as it moves 4.0 m. Calculate
the work done on the car by the truck.
Ex. 4 Calculate the work done by a horse that exerts
an applied force of 100. N on a sleigh, if the harness
makes an angle of 30.o with the ground, and the sleigh
moves 30. m across a flat, level ice surface.
Ex. 5 A 50. kg crate is pulled 40. m along a horizontal
floor by a constant force exerted by a person,
Fp = 100. N, which acts at 37o angle. The floor is rough
and exerts a friction force Ff = 50. N. Determine the
work done by each force acting on the crate, and the
net work done on the crate.
Ex. 6 Determine the work a person must do to carry a
15.0 kg backpack up a hill of height 10.0 m. Determine
also the work done by gravity and the net work done on
the backpack. Assume the motion is smooth and at a
constant velocity.
Machines
- whether powered by people or engines, machines
make our tasks easier.
- a machine eases the load either by changing the
magnitude or direction of the force. It does not
change the amount of work done.
Example. A bottle opener. You lift the handle of the
opener and it lifts the cap off.
The work you do to lift the handle is the input work,
Wi.
The work the machine does is the output work, Wo.
Work is the transfer of energy by mechanical means.
The output work can never be greater than the input
work. The machine aids in the transfer of energy from
you to the cap. The cap cannot receive more energy
than you put into the machine.
The force you exert on a machine is the effort force,
Fe.
The force exerted by the machine is the resistance
force, Fr.
The mechanical advantage of the machine, AMA (or
MA) is:
F
MA  r
Fe
the ratio of the resistance force to the effort force.
Many machines will exert a MA greater than 1 because
it decreases the force you apply.
In terms of work,
Wo  Fr d r
Wi  Fe d e
Wi  Wo
Fe d e  Fr d r
d
Fr
 e
Fe
dr
MA in terms of force
Ideal mechanical advantage is found by using the
measured distances moved.
Actual mechanical advantage is found using the
measured forces exerted.
In a real machine, some input work is lost and
therefore, not equal to the output work.
- losses from energy transformed to heat..
efficiency 
Wo
x100%
Wi
efficiency 
MA
x100%
IMA
All machines are made from six simple machines.
These are *pulleys, *levers, wheel and axle, screws,
wedges, and *incline planes.
Pulleys
To calculate the ideal mechanical advantage of a pulley,
you count the number of supporting ropes except the
effort rope if it is being pulled down.
MA =
Incline Plane
To find the IMA of an incline plane,
IMA 
de
dR
de
dR
Levers
To determine the IMA of a lever,
IMA 
de
dR
Levers are classified as first, second, or third class.
First class: lever with pivot between the load and
effort.
Second class: lever with load between pivot and effort.
Third class: lever with effort between pivot and load.
scissors
nut crackers
fishing rod
Wedge
It is a double incline plane used to split something.
Wheel and Axle
The MA can be found by knowing the radius of the
wheel and the radius of the axle.
MA 
Fr
r
 wheel
Fe
raxle
Screw
To find the IMA, the radius of the bit and the
distance between each thread is needed.
2r
IMA 
pitch
Ex.1. A sledge hammer is used to drive a wedge into a
log to split it. When the wedge is driven 20. cm into
the log, the log is separated a distance of 5.0 cm. A
force of 1.9x104 N is needed to split the log and the
sledge exerts a force of 9.8x103 N.
a) Find IMA
b) Find MA
c) Find efficiency
Ex. 2. A worker uses a pulley system to raise a 225 N
carton 16.5 m. A force of 129 N is exerted on the
rope and the rope is pulled 33.0 m.
a) Find MA
b) Find efficiency
Ex.3. A boy exerts a force of 225 N on a lever to raise
a 1.25x103 N rock a distance of 0.13 m. If the
efficiency of the lever is 88.7%, how far did the
boy move his end of the lever?
Energy
Doing work means you have expended energy doing
something.
In physics, that expended energy means a force was
applied.
There is not much difference between work and
energy.
 In order to do work, an object must have energy
 In order to have energy, an object must have work
done on it.
ENERGY - the measure of a system's ability to do
work. Energy is classified into two terms, potential
energy and kinetic energy.
Potential energy - the energy stored in a body or
system as a consequence of its position, shape, or
form.
Kinetic energy - energy of motion.
Work is the transfer of energy by mechanical means.
When work is done, energy can be transferred from
potential to kinetic energy (kicking a football).
Kinetic energy:
KE 
1
mv 2
2
You can give an object more kinetic energy by
doing more work on it.
In fact, W = KE
Not all objects are at rest. They may already have
kinetic energy when additional work is done on
them.
Wnet  KE f  KEi  KE
Work-energy theorem: the net work done on an object
is equal to its change in kinetic and potential energies.
Potential Energy:
PE  mgh
Energy is transferred from kinetic to potential and
back to kinetic. We describe the total energy, E, as:
ET  PE  KE
The height of where an object is measured from is the
reference level.
Conservation of Energy
Law of Conservation of Energy: within a closed,
isolated system, energy can change form, but the
total amount of energy is constant.
- energy can neither be created or destroyed.
E1  E2
KE1  PE1  KE2  PE2
Ex. 1. A 145 g baseball is thrown with a speed of 25
m/s.
a) What is its KE?
b) How much work was done to reach this speed
starting from rest?
Ex.2. How much work is required to accelerate a
1000. kg car from 20. m/a to 30. m/s?
Ex. 3. A 1000. kg car moves from point A to point B
and then point C. The vertical distance between A
and B is 10. m and between A and C is 15. m.
B
A
C
a) What is the PE at B and C relative to A?
b) What is the PE when it goes from B to C?
c) Repeat a) and b) but take the reference level at C.
Ex. 4. A roller coaster is shown below. Assuming
there is no friction, calculate the speeds at points
B,C, and D if it has a speed of 1.8 m/s at A.
A
C
D
30. m
25 m
12 m
B
Ex. 5 (friction) A girl has a mass of 28 kg. She
climbs a 4.8 m ladder of a slide, and reaches a
velocity of 3.2 m/s at the bottom of the slide. How
much work was done by friction on the girl?
Ex. 6 A 2.75 kg box is at the top of a frictionless
incline. What is the potential energy of the box with
respect to the bottom of the incline?
10.0 m
7.00 m
Ex. 7 A heavy box slides down a frictionless incline.
If the box starts from rest at the top of the incline,
what is its speed at the bottom?
12.0 m
30.0o
Elastic Potential Energy
Many objects can stretch, compress, or change shape
in many ways, but if it returns to its original
condition, it is said to be elastic.
When an object continues to move when the force is
removed, there must have been energy stored in the
object due to its condition. This is elastic potential
energy.
Hooke’s Law
This explains the relationship between the extension
of a spring and the force exerted on it.
Springs can be stretched or compressed and the
force that will restore it to its original state is the
restoring force. It acts in the opposite direction to
the direction that the spring compresses or
stretches.
The restoring force and displacement are
proportional, the graph represents a linear curve.
y = mx + b
The slope of the line (m) represents the spring
constant, k (N/m).
The spring constant is a measure of the stiffness of
the spring.
F  kx
F  kx
F: the restoring force (N)  -kx
F: the applied force (N)  kx
k: spring constant (N/m)
x: extension / displacement (m)
Area is the Ep
F (N)
X (m)
Area under the curve is
1 Fx  E pe
2
F  kx
E pe  1 kx2
2
Ex. 1 A 0.25 kg mass hangs on the end of a spring. What is its
extension if it has a spring constant of 48 N/m?
Ex. 2 How much energy does a bow have when pulled back 8.0 cm if
it has a force constant of 160 N/m?
Now, conservation of energy may incorporate the three types
of mechanical energy: kinetic, gravitational potential, and
elastic potential.
ET 1  ET 2
KE1PE1EE1  KE2PE2EE2
But, not all types of energy are present in a problem.
Ex.1 A 4.0 kg block slides across a frictionless table with a
velocity of 5.0 m/s into a spring with a stiffness of 2500
N/m. How far does the spring compress?
Ex. 2 A 70. kg person bungee jumps off of a 50. m bridge
with his ankles attached to a 15 m long bungee cord.
Assume the person stops at the edge of the water and he
is 2.0 m tall, what is the force constant of the bungee
cord?