Chapter 5 Work and Energy

Part 1

Work

Section 1 Objectives

• Recognize the difference between the scientific and the ordinary definitions of work.

• Define work by relating it to force and displacement.

• Identify where work is being performed in a variety of situations.

• Calculate the net work done when many forces are applied to an object.

Definition of Work

• Clip 595

• Work is done on an object when a force causes a displacement of the object.

• Work = Force X Distance– w = Fd

• Work can only be done in the direction of the force.

Work con’t

• Is there work being performed?

• Why or why not

Work con’t

• What happens when you apply a force at an angle?

• Imagine you are pushing a crate across the floor.

d

F

θ

Work con’t

• Only the horizontal component of you applied force causes a displacement.

• Work in our crate problem is – W = Fdcosθ

• If many forces are acting on an object then we write the equation as

• Wnet = Fnetdcosθ

SI Units for Work

• Work has the dimensions of force times length.

• So, work has the units of Newton x meter or Joules

• Work is positive when displacement is in the same direction of the force, and negative when opposite of the force.

Sample Problem A

• How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50 N at an angle of 30.0° above the horizon?

• A tugboat pulls a ship with a constant net horizontal force of 5000 N and causes a ship to move through a harbor. How much work is done on the ship if it moves a distance of 3.00 km?

• If 2.0 J of work is done in raising an 180 g apple, how far is it lifted?

Today’s Homework

• P. 162 2,3

• P. 163 1-6

• P. 184 1-10

Section II

Energy

Section II Objectives

• Identify several forms of energy.• Calculate kinetic energy for an object• Apply the work-kinetic energy theorem to

solve problems.• Distinguish between kinetic and potential

energy• Classify different types of potential energy• Calculate the potential energy associated

with an objects position.

Kinetic Energy

• Kinetic energy is associated with an object in motion.

• Kinetic energy depends on speed and mass.

• KE = ½ mv2

– Kinetic energy = ½ X mass X (speed)2

• Clip 318

Sample Problems B

• A. 7.0kg bowling ball moves at 3.00 m/s. How fast must a 2.45 g table tennis ball move in order to have the same kinetic energy as the bowling ball?

• What is the speed of a .145 kg baseball if its kinetic energy is 109J?

The Work-Energy Theorem

• Defined as– The net work done by all the forces acting on

an object is equal to the change in the object’s kinetic energy.

– Wnet = ∆KE = ½ mvf

2 – ½ mvi2

Sample Problem C

• On a frozen pond, a person kicks a 10.0 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.

• A 2000 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by the traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Use the work-kinetic energy theorem to determine how far the car must travel for its speed to reach 2.0 m/s.

• A 75 kg bobsled is pushed along a horizontal surface by two athletes. After the bobsled is pushed a distance of 4.5 m starting from rest, its speed is 6.0 m/s. Find the magnitude of the net force on the bobsled.

Potential Energy

• Potential energy is stored energy. It is energy associated with an object because of the position, shape, or condition of the object.

• Gravitational potential energy depends on height from zero level.

• PEg = mgh– Gravitational potential energy

= mass X gravity X height• PEelastic = ½ kx2

– Elastic potential energy = ½ spring constant X (distance)2

• Clip 320 & 321

Sample Problem D

• A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps off a bridge spanning a river from a height of 50.0m. When he finally stops, the cord has a stretched length of 44.0m. Treat the stuntman as a point mass, and disregard the weight of the bungee cord. Assuming the spring constant of the bungee cord is 71.8 N/m, what is the total potential energy relative to the water when the man stops falling?

• The staples inside a stapler are kept in place by a spring with a relaxed length of .115 m. If the spring constant is 51.0 N/m, how much elastic potential energy is stored in the spring when its length is .015 m?

Today’s Homework

• P 166 1, 3, 5

• P 168 1, 3

• P 172 1, 3

• P 172 (Section Review) 1 – 4

• P 184 11 – 14, 23 - 25

Section 3

Conservation of Energy

Section Objectives

• Identify situations in which conservation of mechanical energy is valid.

• Recognize the forms that conserved energy can take.

• Solve problems using the conservation of mechanical energy.

Conserved Quantities

• When something is conserved it means constant.– It can change, but the amount must be the

same.• Example

– Conservation of mass - if a light bulb shatters on the ground. No matter how many pieces the total mass of the pieces will equal the mass of the light bulb.

Mechanical Energy

• Mechanical Energy is defined as the sum of the kinetic and all of the forms of potential energy associated with an object or a group of objects.

• ME = KE + PE• Mechanical energy is conserved

• MEi = MEf

– KEi + PEi = KEf + Pef

– 1/2mvi2 + mghi = 1/2mvf

2 + mghf

• See Clip 567

Mechanical Energy of a Swing

• What is happening to the energy at each point?– 1) KE = 0; ME = PE

51

2

3

4

Sample Problem E

• Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Assume she has the mass of 25.0 kg.

• A 755 N diver drops from a board 10.0 m above the water’s surface. Find the diver’s speed 5.00 m above the water’s surface. Then find the diver’s speed just before striking the water.

• An Olympic runner jumps over a hurdle. If the runner’s initial vertical speed is 2.2 m/s, how much will the runner’s center of mass be raised during the jump?

Today’s Work

• P 177 1 - 5

• P 178 1 - 3

• P 186 26, 28, 30, 31, 33, 34

Section 4

Power

Rate of Energy Transfer

• Power– See Clip 322– The rate at which work is done– A quantity that measures the rate of which work is

done or energy is transformed.– P = W/t

• Power = Work Time Interval

– P = Fv• Power = Force X speed

– The Unit for Power is the watt, W.• ( 1 joule per second)• Horsepower is also a unit for power , it is equal to 746 watts.

Sample Problem F

• A 193 kg curtain needs to be raised 7.5 m, at a constant speed, in as close to 5.0 sec. 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?

• A car with a mass of 1500 kg starts from rest and accelerates to a speed of 18.0 m/s in 12.0 s. Assume the force of resistance remains constant at 400 N during this time. What is the average power developed by the car’s engine?

• How long does it take a 19kW steam engine to do 6.8 x 107 J or work?

Today’s Homework

• P181 Practice F 1, 3, 5

• P181 1, 2, 4

• P 186 35, 36