Work and EnergyAP Physics I

Write down everything you remember about work and energy.

Warm-Up: December 1, 2014

A ball of mass 1.00 kg is thrown directly upward from a height of 1.00 m above the ground. Its initial speed is 100.0 m/s.

a) How high above the ground does the ball go?

b) When does the ball hit the ground?

Warm-Up: December 2, 2014

Energy is the ability to do work. One of the most important concepts in

physics. The total amount of energy in the universe

is constant

Energy

Energy can not be created nor destroyed. Mass is a form of energy.

◦ Einstein’s equation E=mc2

Numerous experimental tests support the principle of conservation of energy.

Conservation of Energy

There are two ways to multiply vectors. Dot product (also called scalar product)

◦ The result is a scalar

Cross product (also called vector product)◦ The result is a vector, perpendicular to both

original vectors◦ The directions is found using the right-hand rule

Vector Multiplication

coscos abbaba

nabnbaba sinsin

Work: The Scientific Definition

AP Physics IOpenStax section 7.1

For work to be done, a force must be exerted and there must be displacement in the direction of the force.

Work is the dot product of force and displacement.

Work is measured in Joules (J).

Work

cosFddFW

A Joule is equal to a Newton times a meter. 1 Joule is not much energy; it would lift a

small 100-gram apple a distance of about 1 meter.

Joule

Examples of Work

Examples of No Work

Example of Negative Work

1. Is work a scalar or a vector?

2. What are the possible values of work?

3. What is the formula to calculate work?

4. What is the SI (mks) unit for work?

Review Questions

a) How much work is done on the lawn mower (from a few slides ago) if he exerts a constant force of 75.0 N at an angle 35° below the horizontal and pushes the mower 25.0 m on level ground?

b) If the person’s average daily intake of food energy is about 10,000 kJ (about 2400 kcal), what percent of his daily intake is required to push the lawn mower in part (a)?

Example

Very little of the energy released in the consumption of food is used to do work.

Even when we “work” all day, less than 10% of our food energy intake is used to do work and more than 90% is converted to thermal energy or stored as chemical energy in fat.

Biology (yuck!)

How much work is done by the boy pulling his sister 30.0 m, with a force of 50.0 N, as shown?

Warm-Up: December 3, 2014

Questions on Work?

Kinetic Energy and the Work-Energy

TheoremAP Physics 1

OpenStax section 7.2

Pushing a lawnmower transfers energy to it. The energy goes to moving the lawnmower

(kinetic energy). Friction within the lawnmower and between

the lawnmower and the ground also transfers energy.◦ Thermal energy leaves as heat.

Work Transfers Energy

Net Workcosnetnet dFW

cosnet madW

cos2

20

2

net dd

vvmW

cos2

1 20

2net vvmW

If net force and displacement are in the same direction (which is a common occurrence), then

Net Work

202net 2

1vvmW

20

2net 2

1

2

1mvmvW

0net KKW

Energy of motion Represented by K or KE Measured in Joules

Kinetic Energy

2

2

1mvK

Applies even for forces that vary and for forces that are not parallel to displacement.

Work-Energy Theorem

0net KKW

Diagram for the next 4 problems

A 30.0 kg package on a roller belt conveyor system is moving at 0.500 m/s. What is its kinetic energy?

You-Try 7.2

a) Calculate the net work done on the package.b) Find the work done by each force, and show

that the total work is equal to the net work found in part a.

You-Try 7.3

a) Calculate the net work done on the package.b) Find the work done by each force, and show

that the total work is equal to the net work found in part a.

You-Try 7.3

Find the speed of the package at the end of the push. Its initial speed was given in You-Try 7.2

You-Try 7.4

How far does the package coast after the push, assuming friction remains constant?

Warm-Up: December 4, 2014You-Try 7.5

Questions on Work-Energy Theorem?

Gravitational Potential Energy

AP Physics 1OpenStax section 7.3

Lifting an object is work done against the gravitational force.

The work done goes into an important form of stored energy, called gravitational potential energy.

Work Done Against Gravity

cosFdW 0cosymgW

mghPEU

h is a change in height, even though Δ is not written

Applies for any path that has a change in height of h, not just for vertical motion.

Gravitational Potential Energy

ymgmghPEU

If an object is dropped from a height h, gravitational force will do work on the object.

This work increases its kinetic energy. This can be expressed as:

This equation is valid when no force besides gravity is acting on the object (or when all other forces are negligible).

Converting Between PE and KE

0

0

KU

KEPE

g

g

Other Forms of the Equation

2200

2200

00

22

2

1

2

1

0

vgyvgy

mvmgymvmgy

KUKU

KU g

A 60.0 kg person jumps onto the floor from a height of 3.00 m. If he lands stiffly, with his knee joints compressing by 0.500 cm, calculate the force on the knee joints.

You-Try 7.6

Such a large force (500 times more than a person’s weight) over a short impact time is enough to break bones.

Biology (yuck!)

a) What is the final speed of the roller coaster shown if it starts from rest and work done by frictional forces is negligible?

b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

You-Try 7.7

a) What is the final speed of the roller coaster shown if it starts from rest and work done by frictional forces is negligible?

b) What is its final speed (again assuming negligible friction) if its initial speed is 5.00 m/s?

You-Try 7.7

1. How does the mass of an object impact the conversion between gravitational potential energy and kinetic energy?

2. Where else did mass not matter?3. How did the dip at the bottom of the first

hill affect the final kinetic energy?4. True or False: If two objects at the same

initial height have speeds that differ by K, then their final speeds at another height will also differ by K.

Review Questions

Questions on PE and KE?

With your group (assigned on the next slide), design an experiment that can demonstrate the conversion between gravitational potential energy and kinetic energy.

Materials allowed:◦ Rulers◦ Meter stick◦ Marble◦ Physics book◦ Stopwatch

Write detailed procedures in your lab notebook, along with lab name, group members, materials used, and discussion of how your experiment demonstrates conservation of energy.

Experimental Design

Group #1 Mark Christin

aJocelyn Wesley

2 Elroi Isabel Peter Foster3 Karla Tong Hector Jeremy4 Justin Diana Shane Erin5 Tiffany Shelby Frank Phat6 Kevin Joseph Regge7 Courtney Angela Paul

Groups

Work Done in Stretching a Spring (GI) [CR6b]

To determine the work done on the spring from force-versus-distance graph of the collected data.

Lab Idea