WORK, POWER, ENERGY
REPORTERS:
KHLAIRE ABEGAIL M. RUPEREZ
WILLOWY COLEEN D. BONCALES
HANZ APPLE M. COSCOS
JULIUS SULAPAS
Work
-quantity that exist whenever a force acting upon an object causes
a displacement.
W=F(cos
)d
(Eqn 8.1)
3 key words
*force
*displacement
*cause.
Unit of work
“J” standard metric unit
1 joule = 1 newton * 1 meter
1 J = 1N * m
~Non-standard units of work~
1. ft-pound
2. Kg*m/s²*m
3. Kg*m²/s²
* work is a force acting upon an object to case a displacement.
When a force acts to cause an object to be displaced, 3
quantities( force, displacement and angle) must be known in
order to calculate the amount of work.
Maximum Work
-work is maximum if the force applied is completely along the
direction of the displacement.
Example of Work (without angle)
A 100 N force is applied
to move a 15 kg object a
horizontal distance of 5
meters at constant speed.
ANSWER
W = (100 N) * (5 m)* cos(0 degrees) = 500 J
The force and the displacement are given in the problem
statement. It is said (or shown or implied) that the force and the
displacement are both rightward. Since F and d are in the same
direction,the angle is 0 degrees.
Example of Work ( with angle)
A 100 N force is applied at
an angle of 30° to the
horizontal to move a 15 kg
object at a constant speed
for a horizontal distance of
5 meter.
ANSWER
W = (100 N) * (5 m) * cos(30 degrees) = 433 J
The force and the displacement are given in theproblem statement. It
is said that the displacement is rightward. It is shown that the force
is 30 degrees above the horizontal. Thus, the angle between F and d is
30 degrees.
Example Lifting Quarter Pounders
If I lift a quarter-pound hamburger with a force of 1 newton up a
distance of one meter, how much work did I do?
Answer
Given:
Force applied F
1 Newton
Distance traveled d
1 meter
Find: Work done
W
Solution
Substituting the given values directly to W=F x d.
Work = F x d
= 1 newton x 1 meter
=1 newton – meter
= 1 joule
Answer: I did one joule of work.
Work done against gravity
W = mg (will be our f)
W=Fxd
= mg x h
Example 8.2 “Saging para climbing”
Eating banana enables a person to perform about 4.0x10^4 J of
work. How high can a 60-kg woman climb if energized by eating a
banana?
Answer
Given:
work that can be done from eating banana W 4.0 x 10^4
Mass of woman m 60 kg
Find: How high a woman can climb from eating a banana (h)?
since the motion is along the vertical, we can use the equation for
work done against gravity, then solve for h.
From W = mgh
Simple Machines
---A machine is anything that makes easier.
2 ways machines help man:
*Some machine help man apply a “greater effective force” on the
object despite applying a lesser amount of force .
*Some machine help move an object over longer distance even if
your work is done over shorter distance.
(Mechanical Advantage) MA = force on the load / force into
machine
= Fout / Fin
Efficiency measures how much of the work you put in gets to the
load.
Efficiency = useful work output/ total work input
=Wout/ Win
*3 simple machine of lever groups
-levers
-wheels
-axles and pulleys
Lever- is a board balanced on a point of support that can be
rotated to lift something.
*3 basic types of levers
- First-class (the longer the better)
- Second-class (short but powerful)
- Third class (distance matters)
*First-class lever, the fulcrum is between the load and the applied
force.
*second-class lever, the load lies between the fulcrum and the
applied force.
*third-class lever, the effort is applied between the load and the
fulcrum, your effort will be greater, but you can move objets
over longer distances.
The Wheel and Axle
Wheel and Axle essentially a modified lever, but using two circles,
one smaller (axle) and one bigger (the wheel) attached in the
middle. It makes it easier to push a car forward than if you had
to slide it along the ground with no wheels. The axle must move
with the wheels.
Every small turn of the axle corresponds to a bigger turn from
the wheel.
Pulley is a rope over a cylinder, which changes the direction of the
force, you pull the rope down and the object moves up.
3 Machines make up the inclined plane group.
-ramps
-wedges
-screws
Inclined Plane makes it easier to move a heavy object up but
lessening the force but making you push over a longer distance
than you would need to lift it.
Inclined Plane is also known as Ramps.
Wedges has 2 parts to consider :
b (base) and h (height)
The Screw has 2 important parts to consider:
p (pitch) and r (radius of the circular head)
Example “Gaining Leverage”
Using a lever how much force is needed to pick up a 100-newton
boulder?
Given: weight of the boulder
Big distance
Small distance
Fi
di
do
100N
1m
0.01
Find: force needed to pick up the boulder Fi.
Solution
little force x big distance = big force x little distance
Fi x di
= Fo x do
Fi x 1m
= 100N x 0.01 m
Fi = 1N
Example 8.4 “Pulley, pulley”
If you put in 200 joules of work to lift a 100 N box 1 meter with a
pulley system.
What is the machine’s efficiency?
Given: Total Work Input
Resisting force
Win
Fout
200J
100N
Distance moved by the applied force dout 1m
Find: Efficiency
Solution
Efficiency = Wout / Win
*solve for Wout
Wout = Fout x dout = 100N x 1m = 100J
*solve for efficiency
100N x 1 meter/ (200 N m) = 0.5
*Percentage Efficiency = 0.5 * 100% = 50%
Power – amount of work done per unit time.
*unit of power
1 watt = 1 J/s
Horsepower (hp) is the traditional unit of power
in engineering.
1 hp = 746 W =0.746 kW
1 kW = 1.34 hp
Example 8.5
An electric motor with an output of 15 kW provides
power for the elevator of a six-story building. If
the total mass of loaded elevator is 1000 kg, what
is the minimum time needed for it to rise 30 m
from the ground floor to the top floor?
Given
Power output
15 kW (P)
Total mass of elevator
1000 kg (m)
Height raised
30 m (h)
Find: Time to rise (t)
15 kW * 1000 watts / 1 kw = 15, 000 watts
*solve for t= W/P
w = mgh (work done)
Substitute t=W/P=mgh/P
t= 1000 kg * 9.8 m/s² * 30m
15,000 Watts
*since 1 watt = 1N*m = 1 kg-m/s²-m = 1 kg-m²/s²
t=1000 kg * 9.8 m/s² * 30m
15,000 kg – m²/s
= 20s
The time needed for the 15 kW motor to raise a 1000-kg
elevator by 30 m is 20s.
Energy- the ability to do work.
2 kind of energy
*potential energy
-is energy that is stored and waiting to be used.
*kinetic energy
- is energy in movement. Has 3 types the
Vibrational (ex. When strumming the guitar),
Rotational (ex. Biking – spinning wheels) and
Translational (ex. Surfing- the surfer’s movement)
*Formula
KE=0.5 mv²
Example:
If you throw a cheeseburger deluxe weighing 0.1 kg at 10
meters per second, how much kinetic energy have I
given it?
Given
Mass of the burger m
0.1 kg
Velocity of the burger v 10 m/s
Find: Kinetic Energy given to the burger (KE)
Solution
KE = 0.5 (0.1 kg) 8 (10 m/s)²
= 5 kg-m²/s²= 5 N-m = 5 J
Answer: You gave that cheeseburger 5 joules of energy by
throwing it.
2 forms of potential energy
*Gravitational Potential Energy
-the energy stored in an object as the result of
its vertical position.
PE grav = mass*g*height (eqn. 8.12)
=w*h
(eqn. 8.13)
Example: (formula: eqn. 8.13)
If you lift a 1-Newton cheeseburger deluxe 1
meter how much gravitational potential
energy have you give it?
Solution
PEgrav = weight (force to lift) x height
= 1 newton x 1 meter = 1 joule
Answer: I gave that burger 1 joule of gravitational
potential energy.
Example: (formula: eqn. 8.12)
What is the gravitational potential energy of a 0.5-kg ball
soon to be dropped from a 15 m high building?
Given
Mass of the ball
m
0.5 kg
Height of the ball h 15 m
Find: Gravitational potential energy of the ball (PEgrav)
Solution
Pegrav = mgh = 0.5 kg (9.8m/s²) (15m) = 73.5 J
Answer:73.5 J
*Elastic Potential Energy
-the energy stored in elastic materials as the
result of their stretching or compressing.
-can be stored in rubber hands, bungee chords
and trampolines.
Question 1: A compressed spring has potential energy of
20 J. If the spring constant of the spring is 200 N/m,
find the displacement of the spring?
Solution:
Given: Potential energy P.E = 20 J,
Spring Constant k = 200 N/m,
The Potential energy is given by P.E = 1/2 kx²
X=
X=
X=0.4 m