UNIT 4

Work and Energy

Energy Considerations

Energy cannot be created, nor can it be destroyed, but it can change from one form into another.It is essential to the study of physics and then it is applied to chemistry, biology, geology, astronomy

In some cases it is easier to solve problems with energy then Newton’s laws

Forms of Energy

Mechanical focus for now

chemical electromagnetic Nuclear Heat Sound

Consider the following situations … A student holds a heavy chair at arm’s

length for several minutes. A student carries a bucket of water along

a horizontal path while walking at constant velocity.

Do you think that these situations require a lot of “work”?

Work

Provides a link between force and energy

The work, W, done by a constant force on an object is defined as the product of the component of the force along the direction of displacement and the magnitude of the displacement

Work, cont

F cos θ is the component of the force in the direction of the displacement Process Called the Dot Product (we will get to

the Dot Product in AP Physics) Δ x is the displacement

Units of Work• SI

▫ Newton • meter = Joule N • m = J

More about Work

This gives no information about the time it took for the displacement to occur the velocity or acceleration of the object

Scalar quantity The work done by a force is zero when the

force is perpendicular to the displacement cos 90° = 0

If there are multiple forces acting on an object, the total work done is the algebraic sum of the amount of work done by each force

More About Work, continued

Work can be positive or negative Positive if the force and the displacement

are in the same direction Negative if the force and the displacement

are in the opposite direction• Work is positive when lifting the box• Work would be negative if lowering the box

When Work is Zero

• Displacement is horizontal• Force is vertical• cos 90° = 0

Example (pg 169)

How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0o above the horizontal?

YOU TRY! (pg 170 #1)

A tugboat pulls a ship with a constant net horizontal force of 5.00 x 103 N and causes the ship to move through a harbor. How much work is done on the ship if it moves a distance of 3.00 km?

Kinetic Energy

Once again Energy associated with the motion of an object

Kinetic Energy: The energy of an object due to its motion

The equation is:

The unit for KE is JOULES (J).

Example (pg 173)

A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have?

How fast must a 2.45 g table-tennis ball move in order to have the same kinetic energy as the bowling ball?

Work-Kinetic Energy Theorem The theorem stating that the net work

done on an object is equal to the change in the kinetic energy of the object.

Wnet=ΔKE

Example (pg. 175)

On a frozen pond, a person kicks a 10 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is .10?

Potential Energy

Potential energy is associated with the position of the object within some system Potential energy is a property of the

system, not the object A system is a collection of objects or

particles interacting via forces or processes that are internal to the system

Gravitational Potential Energy Gravitational Potential Energy is the

energy associated with the relative position of an object in space near the Earth’s surface Objects interact with the Earth through the

gravitational force Actually the potential energy of the earth-

object systemPEg = mgy

Example (pg. 180 #5)

A spoon is raised 21.0 cm above a table. If the spoon and its content have a mass of 30.0 g, what is the gravitational potential energy associated with the spoon at that height relative to the surface of the table?

5.3: Conservation of Energy

Conserved quantities: conserved means that it remains constant.

If we have a certain amount of a conserved quantity at some instant of time, we will have the same amount of that quantity at a later time. This does not mean that the quantity

cannot change form during that time. EXAMPLE: Money

Mechanical Energy

Mechanical Energy: the sum of kinetic energy and all forms of potential energy associated with an object or group of objects.

Mechanical Energy is CONSERVED (in the absence of friction)

MEi = MEf

KEi + PEi = KEf + PEf

Energy Tables

To simplify our method of analyzing these situations, we will use an energy table. Each variable has to be found at each point.

Remember: v = 0 means zero KE h = 0 means zero PEg

Example 1

Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is the speed at the bottom of the slide? Assume she has a mass of 25 kg.

Example 2

Assume no friction. Solve for each blank. “ME” just is the total energy (ET). At position 3, assume the skater is not moving.

Power

The rate at which energy changes (specifically work) is called power.

We designate power in equations with a P. Power is measured in Watts (W).

P = W/tP = Power (W)W= Work (J)t= time (sec)

Power (another equation)

We can also define power in the following way …

P = FvP=Power (W)F= Force (N)

v= velocity (m/s)

Power

Machines with different power ratings do the same work in different time intervals. So, work is the same but the time it takes

to do that work is either longer or shorter depending upon the power.

While the SI Unit for Power is WATTS (W), sometimes power will be measured in horsepower. One horsepower (hp) = 746 watts

Example 1

A 193 kg curtain needs to be raised 7.5 m, at constant speed, in as close to 5.0 s as possible. The power ratings for three motors are listed as 1.0 kW, 3.5 kW and 5.5 kW. Which motor is best for the job?

Example 2

A 1.0 x 103 kg elevator carries a maximum load of 800 kg. A constant frictional force of 4.0 x 102 N retards the elevators motion upward. What minimum power, in kilowatts, must the motor deliver to lift the fully loaded elevator at a constant speed of 3.00 m/s?

Conservation of Energy Review

Solve for all the blanks using an Energy Table

Hooke’s Law

Fs = - k x Fs is the spring force k is the spring constant

It is a measure of the stiffness of the spring A large k indicates a stiff spring and a small k indicates

a soft spring

x is the displacement of the object from its equilibrium position

The negative sign indicates that the force is always directed opposite to the displacement

Hooke’s Law Force

The force always acts toward the equilibrium position It is called the restoring force

The direction of the restoring force is such that the object is being either pushed or pulled toward the equilibrium position

F is in the opposite direction of x

Hooke’s Law – Spring/Mass System When x is positive

(to the right), F is negative (to the left)

When x = 0 (at equilibrium), F is 0

When x is negative (to the left), F is positive (to the right)

Elastic Potential Energy

A compressed spring has potential energy The compressed spring, when allowed to

expand, can apply a force to an object The potential energy of the spring can be

transformed into kinetic energy of the object

Elastic Potential Energy

The energy stored in a stretched or compressed spring or other elastic material is called elastic potential energy

Pes = ½kx2

The energy is stored only when the spring is stretched or compressed

Elastic potential energy can be added to the statements of Conservation of Energy and Work-Energy

PEs Example 1

If you compress as spring with spring constant 4 N/M, 50 cm how much energy is stored?

Fs Example 1

If a mass of .55 kg attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

Nonconservative Forces

A force is nonconservative if the work it does on an object depends on the path taken by the object between its final and starting points.

Examples of nonconservative forces kinetic friction, air drag, propulsive forces

Friction and Energy

The friction force is transformed from the kinetic energy of the object into a type of energy associated with temperature the objects are warmer than they were

before the movement Internal Energy is the term used for the

energy associated with an object’s temperature

Nonconservative Forces w/ Energy When nonconservative forces are

present, the total mechanical energy of the system is not constant

The work done by all nonconservative forces acting on parts of a system equals the change in the mechanical energy of the system

E n e r g yW a t i v en o n c o n s e r v

Problem Solving w/ Non-conservative Forces

Define the system Write expressions for the total initial

and final energies Set the Wnct equal to the difference

between the final and initial total energy Follow the general rules for solving

Conservation of Energy problems