Download 2a-Work Power Simple Machines - MrD-Home

Work
A force applied in the direction of a
displacement
 Area under Force-Displacement graph
 A scalar quantity

Work = Force x Displacement x cos θ
W = Fdcosθ (units: 1 Nm = 1 Joule)
Examples
Example 1:
How much work is done by a crane that lifts 120 kg up a
distance of 75 m?
Example 2:
A student pulls a box with a force of 25 N at an angle of 25o
with the horizontal. The box moves 12 m along the ground.
How much work is done?
Power


Rate of doing work (or rate of using energy)
Units: Watt (1 W = 1 J/s) or hp (1 hp = 746 W)
Power = Work = Energy used
time
time
P = W = Fd = Fv
t
t
Example:
Find the power output of a 60.0 kg athlete who climbs the
Grouse Grind in 40.0 minutes. (elev. gain = 800.0m)
Example:
Find the power output of a 60.0 kg athlete who climbs the
Grouse Grind in 40.0 minutes. (elev. gain = 800.0m)
Power = Work = (mg)d = 60 x 9.8 x 800 = 196 W
time
t
2400
(in seconds)
In horsepower:
196 W * (1 hp / 746 W)
= 0.26 hp
Pg. 204 Lab – Your Power
What do you think?
Which of the following statements are true about work?
Work is a form of energy.
B. A Watt is the standard metric unit of work.
C. Units of work would be equivalent to a Newton
times a meter.
D. A kg∙m2/s2 would be a unit of work.
E. Work is a time-based quantity; it is dependent
upon how fast a force displaces an object.
F. Superman applies a force on a truck to prevent
it from moving down a hill. This is an example of
work being done.
A.
A. TRUE - Work is a form of energy, and in fact it has units
of energy.
B. FALSE - Watt is the standard metric unit of power; Joule is
the standard metric unit of energy.
C. TRUE - A N ∙ m is equal to a Joule.
D. TRUE - A kg ∙ m2/s2 is a mass unit times a speed squared
unit, making it a kinetic energy unit and equivalent to a Joule.
E. FALSE - Work is not dependent on how rapidly the force
displaces an object; power is time-based and calculated by force
multiplied by speed.
F. FALSE - Since Superman does not cause a displacement,
no work is done; he is merely holding the car to prevent its
descent down the hill.
G. An upward force is applied to a bucket as it is
carried 20 m across the yard. This is an example of work
being done.
H. A force is applied by a chain to a roller coaster car to
carry it up the hill of the first drop of the Shockwave
ride. This is an example of work being done.
I. The force of friction acts upon a softball player as
she makes a headfirst dive into third base. This is an
example of work being done.
J. An eraser is tied to a string; a person holds the string
and applies a tension force as the eraser is moved in a
circle at constant speed. This is an example of work
being done.
G. FALSE - The upward force does not cause the
horizontal displacement so this is a NON-example of
work.
H. TRUE - There is a component of force in the
direction of displacement and so this is an example of
work.
I. TRUE - There is a force and a displacement; the
force acts in the opposite direction as the
displacement and so this force does negative work.
J. FALSE - For uniform circular motion, the force
acts perpendicular to the direction of the motion and
so the force never does any work upon the object.
Work Concepts:
Which of the following statements are true about
power? Include all that apply.
A.
B.
C.
D.
Power is a time-based quantity.
Power refers to how fast work is done upon
an object.
Powerful people or powerful machines are
simply people or machines which always do a
lot of work.
A force is exerted on an object to move it at
a constant speed. The power delivered by
this force is the magnitude of the force
multiplied by the speed of the object.
E.
F.
The standard metric unit of power is the Watt.
If person A and person B do the same job but
person B does it faster, then person A does
more work but person B has more power.
G.
The Newton ∙ meter is a unit of power.
H.
A 60-kg boy runs up a 2.0 meter staircase in 1.5
seconds. His power is approximately 80 Watt.
A 300-Newton force is applied to a skier to
drag her up a ski hill at a constant speed of 1.5
m/s. The power delivered by the toe rope is
450 Watts.
I.
Answer: ABDEI
A. TRUE - Power is a rate quantity and thus time-based.
B. TRUE - This is the definition of power.
C. FALSE - This is not always the case. A machine can do a lot of work but if it
fails to do it rapidly, then it is not necessarily powerful. In fact two machines can
do the same task (and therefore the same work), yet they can have drastically
different power ratings.
D. TRUE - An equation for computing work in constant speed situations is
P=F•v.
E. TRUE - Watt is the unit of power? Yes!!
F. FALSE - Vice versa. If two people do the same job, then they're doing the
same amount of work. The person who does it fastest generates more power.
G. FALSE - A N•m is a Joule and that is a unit of work (not power). Think force
(N) times distance (m); that's work (J).
H. FALSE - The work would be (m•g)•d or approximately 1200 J. The power is
work divided by time - 1200 J/1.5 s = 800 W.
I. TRUE - Since force and speed are given, use Power = F•v. The calculation
yields 450 W.
3. Positive, Negative, or No work?
A. A cable is attached to a bucket and the force of tension is used to
pull the bucket out of a well.
B. Rusty Nales uses a hammer to exert an applied force upon a
stubborn nail to drive it into the wall.
C. Near the end of the Shockwave ride, a braking system exerts an
applied force upon the coaster car to bring it to a stop.
D. The force of friction acts upon a baseball player as he slides into
third base.
E. A busy spider hangs motionless from a silk thread, supported by the
tension in the thread.
F. In baseball, the catcher exerts an abrupt applied force upon the ball
to stop it in the catcher's mitt.
G. In a physics lab, an applied force is exerted parallel to a plane
inclined at 30-degrees in order to displace a cart up the incline.
H. A pendulum bob swings from its highest position to its lowest
position under the influence of the force of gravity.
Answers:
A. The force is upwards and the displacement is upwards. When the force
and the displacement act in the same direction, positive work is done.
B. The force is horizontal and the displacement is horizontal. When the
force and the displacement act in the same direction, positive work is
done. (It is true that the wall is doing negative work upon the nail but
this statement is about the hammer's force on the nail.)
C. The force is backwards and the displacement is forwards. When the
force and the displacement act in the opposite direction, negative
work is done.
D. The force is backwards and the displacement is forwards. When the
force and the displacement act in the opposite direction, negative
work is done.
E.
F.
G.
H.
If the force does not cause the object to be displaced (the object
hangs motionless), then no work is done.
The force is backwards and the displacement is forwards. When
the force and the displacement act in the opposite direction,
negative work is done.
The force is upwards and parallel to the incline and the
displacement is in the same direction parallel to the incline. When
the force and the displacement act in the same direction, positive
work is done.
As the bob swings downwards from its highest position, the
motion is downwards (and rightwards); the force is also
downwards and as such there is a component of force in the
direction of motion. When the force and the displacement act in
the same direction, positive work is done. (Note that if the bob
was swinging upwards from its lowest position to its highest
position, then gravity would be doing negative work.)
Simple Machines
A machine is a device that helps make work
easier (not less of it!) to perform by
accomplishing one or more of the following
functions:
 transferring
a force from one place to
another
 changing the direction of a force
 decreasing the magnitude of a force
 increasing the distance or speed of a
force
The 6 Simple Machines
Inclined Plane
Screw
Pulley
Lever
Wedge
Wheel and Axle
Mechanical Advantage (MA)
Wout = Win
Fout x Dout = Fin x Din
Fout = Din
Fin
Dout
MA = Output = Fout
Input
Fin
Levers
3 Types of levers: The class of a
lever is determined by the location
of the effort force (E) and the load
(R) relative to the fulcrum (F).
First Class Lever
.

Common examples of firstclass levers include
crowbars, scissors, pliers, tin
snips and seesaws.



Set up a class 1 lever with the fulcrum at the
middle of the meter stick
Hang a 1 kg mass near one end. This will be
your Load force
Balance the meter stick by adding a 200 g mass
on the other side of the fulcrum. This is your
Effort force
What is mechanical advantage
of your lever?

Torque ()




A ‘twist’ or rotation that is caused by a force acting at a
distance from a pivot (fulcrum)
Equal to the product of force and distance from a
fulcrum.
Torque is a vector (CW or CCW)
Units: N ∙ m (Same as work but NOT the Joule!)
 = Fd
: Torque (Nm)
F: Force (acting perpendicular to meter stick) (N)
d: Displacement vector from pivot to force (m)
Lab Activity
1. Set up a meter stick in equilibrium with a force hanging
from either side of the fulcrum.
2. For each mass: Calculate the Force, measure the Distance
from the fulcrum, and calculate the Torque
3. Fill in the table below for 3 separate trials (different
masses /distances from fulcrum.
Trial
5.
Effort Force
Effort
Distance
1
Load Force
Load
Distance
2
1
2
3
Driving Question: How do the two torques compare for
each trial? Why?

Challenge: Using your lab equipment, can you
figure out the mass of the meter stick?
No….you cannot use a scale to measure it!
Second Class Lever

Examples of
second-class levers
include nut crackers,
wheel barrows,
doors, and bottle
openers.



Set up a Class 2 lever similar to what is shown
below
Hang a 500 g mass (Load) between the Effort
force and the fulcrum
Using a string and a force meter, measure the
Effort force required to lift the Load
What is the mechanical
advantage of the lever?

1.
2.
What is the Torque due to the effort force?
What is the Torque due to the load force?
Set up 2 other class 2 levers. Repeat steps 1 and 2.
What do you notice about the Torques?
Trial
1
2
3
Effort Force
Effort
Distance
1
Load Force
Load
Distance
2
Third Class Lever

Examples of
third-class
levers include
tweezers, biceps,
and hammers
Inclined Planes


A flat surface that is higher
on one end
Makes the work of moving
things easier because you
need less force
Wedges


Two inclined planes
joined back to back.
Wedges are used to split
things.
Pulleys


Pulley are wheels and
axles with a groove
around the outside
A pulley needs a rope,
chain or belt around the
groove to make it do work
Diagrams of Pulleys
Fixed pulley:
Movable Pulley:
A fixed pulley changes the
direction of a force; however, it
does not create a mechanical
advantage.
The mechanical advantage of
a moveable pulley is equal to
the number of ropes that
support the moveable pulley.
COMBINED PULLEY


The effort needed to
lift the load is less
than half the weight
of the load.
The main
disadvantage is it
travels a very long
distance.
Rube Goldberg Machines




Rube Goldberg machines are
examples of complex machines.
All complex machines are made
up of combinations of simple
machines.
Rube Goldberg machines are
usually a complicated
combination of simple machines.
By studying the components of
Rube Goldberg machines, we
learn more about simple
machines