WORK, ENERGY AND POWER
OBJECTIVES
✔ To define mechanical work and compute the work done in various situations.
✔ To explain the work-energy theorem and apply it in problem solving.
✔ To compute power in watts and horsepower
✔ Discuss and define Kinetic Energy and Potential Energy
WHAT IS WORK?
• In physics, work is the energy transferred to or from an object via the
application of force along a displacement.
• In its simplest form, it is often represented as the product of force and
displacement.
WHAT IS WORK?
• Work is said to be done when a body or object moves with the application of
external force.
• We can define work as an activity involving a movement and force in the
direction of the force.
• For example, a force of 30 newtons (N) pushing an object 3 meters in the
same direction of the force will do 90 joules (J) of work.
FORMULA
• When we kick a football, we are exerting an external force called F and due
to this force (kick), the ball moves to a certain distance.
• This disposition of ball from position A to B is known as displacement (d).
This work is said to be done and can be calculated as W = F × d
EXAMPLE 1
Steve exerts a steady force of magnitude 210N on the stalled car as he pushes it a distance of
18m. The car also has a flat tire, so to make the car track straight, Steve must push at an angle
of 30º to the direction of motion.
(a) How much work does Steve do?
(b)
In a helpful mood, Steve pushes a second stalled car with a steady force F=(160N)i –
(40N)j. The displacement of the car is s=(14m)i + (11m)j. How much work does Steve do
in this case?
SOLUTION
WORK: POSITIVE, NEGATIVE, OR ZERO
TOTAL WORK
1. Compute the work done by each separate force. Take the algebraic sum of
all the work done by the individual forces.
2. Compute the vector sum of the forces (Net forces) then use the vector sum
in the formula for work.
EXAMPLE 2
Calculate the work done by a 2.3-N force (directed at a 33° angle to the
vertical) to move a 500 gram box a horizontal distance of 400 cm across a
rough floor at a constant speed of 0.5 m/s.
SOLUTION
EXAMPLE 3
Two tugboats pull a disabled supertanker. Each tug exerts a constant force of 1.80x106
N, one 14º west of north and the other 14º east of north, as they pull the tanker 0.75km
toward the north. What is the total work they do on the supertanker?
SOLUTION
WHAT IS ENERGY?
Energy is the ability to perform work. Energy can neither be created nor destroyed. It
can only be transformed from one kind to another. The unit of Energy is same as of
Work i.e. Joules. Energy is found in many things and thus there are different types of
energy.
All forms of energy are either kinetic or potential. The energy in motion is known as
Kinetic Energy whereas Potential Energy is the energy stored in an object and is
measured by the amount of work done
KINETIC ENERGY
THE WORK-ENERGY THEOREM
• The total work done on a body by external force is related to the body’s
displacement – that is to change its position.
• But the total work is also related to changes in the speed of the body.
THE WORK-ENERGY THEOREM
Kinetic energy depends only on the particle’s mass and speed, not its direction
of motion. Kinetic energy can never be negative, and it is only zero when the
particle is at rest.
The work done by the net force on a particle equals the change in the particle’s
kinetic energy, where the result is the work-energy theorem.
EXAMPLE 4
(a) How many joules of kinetic energy does a 750-kg automobile travelling at a
typical highway speed of 65mi/h have?
(b) By what factor would its kinetic energy decrease if the car traveled half as
fast?
(c) How fast (in mi/h) would the car have to travel to have half as much
kinetic energy as in part (a)?
SOLUTION:
SOLUTION:
WORK AND ENERGY WITH VARYING
FORCES
When a force varies as it pushes or pulls an object, one cannot simply
calculate work as the product
Instead, one must integrate the force through the distance over
which it acts
For a spring, the force required to stretch a spring is given as F = k x,
Where k is the spring constant (N/m) This is based from Robert
Hooke’s study that the force needed to stretch a spring is directly
proportional to the elongations.
WORK AND ENERGY WITH VARYING
FORCES
To stretch a spring, we must do work.
If initially the spring is already stretched a
distance x1, the work we must do to stretch
it to a greater elongation x2,
EXAMPLE 5
A woman weighing 600N steps on a bathroom scale containing a stiff spring.
In equilibrium the spring is compressed 1.0cm under her weight. Find the force
constant of the spring and the total work done on it during the compression.
SOLUTION
EXAMPLE 6
To stretch a spring 3.00cm from its unstretched length, 12.0J work must be
done.
(a) What is the force constant of this spring?
(b) what magnitude force is needed to stretch the spring 3.00cm from its
unstretch length?
(c) How much work must be done to compress this spring 4.00cm from its
unstretched length, and what force is needed to stretch it this distance?
SOLUTION
SOLUTION
WHAT IS POWER?
We can define power is the rate of doing work. It is the amount of energy
consumed per unit time.
Therefore, it can be calculated by dividing work done by time. The formula for
power is given as:
POWER
EXAMPLE 7
Each of the two jet engines in an airliner develops a thrust ( a forward force on
the airplane) of 197, 000N. When the airplane is flying at 250 m/s, what
horsepower does each engine develop?
SOLUTION
EXAMPLE 8
How many joules of energy does a 100-watt light bulb use per hour?
How fast would a 70-kg person have to run to have that amount of kinetic
energy?
SOLUTION
EXAMPLE 9
A tandem (two-person) bicycle team must overcome a force of 165N to
maintain sa speed of 9.00m/s. Find the power required per rider, assuming that
each contributes equally. Express your answer in watts and horsepower.
SOLUTION
POTENTIAL
ENERGY
WORK, ENERGY AND POWER