Physics  Chapter 5  Lesson 37: Work  Notes 
LEARNING TARGET JOURNAL
NOTES
 Work is defined as the product of the magnitude of a force, F, and the displacement it creates, Δx.
If the force is at an angle, then only the component of the force that is parallel to Δx is doing the work.
 θ is the angle between the force, F, and the displacement, Δx.
 Meaning work has no defined direction just a magnitude.
 The work done by a force is positive when F is in the same direction as Δx.
 The work done by a force is negative when F is in the opposite direction of Δx.
 The variable for work is W.
 The SI unit for work is the Joule. (J)
 Which is equivalent to a N·m
 If there is more than one force acting on the object, then use the net force to find the net work
 If there is no displacement, there is no work done.
 Friction is an example of a force that will perform negative work on an object.

EXAMPLE 1 – Find the work done in the following problems.
 A horizontal force of 150 N is used to push a 40.0 kg packing crate a distance of 6.00 m on a rough horizontal surface. If the crate moves with constant velocity, calculate the work done by the force.


EXAMPLE 2 – Find the indicated value.
 A 0.075 kg ball in a kinetic sculpture is raised 1.32 m above the ground by a motorized vertical conveyor belt. Ignoring the internal friction of machine, find the work done by the conveyor belt.

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

 A worker pushes a 1.50 × 103 N crate with a horizontal force of 345 N a distance of 24.0 m. Assume the coefficient of kinetic friction between the crate and the floor is 0.220. How much work is done by the floor on the crate by way of friction?

HOMEWORK 
Physics  Chapter 5  Lesson 38: Kinetic Energy  Notes 
LEARNING TARGET JOURNAL
 What is energy?
 What is kinetic energy?
 What is potential energy?

NOTES
 Energy is defined as an object’s ability to perform work.
 Energy is also a scalar quantity
 The SI unit for energy is the same as that for work, Joule. (J)
 Mechanical energy is the sum of all forms of energy associated with motion.
 Mechanical energy comes in two basic forms.
 Kinetic energy
 Potential energy
 Kinetic energy is the energy of an object in motion.
 Kinetic energy is proportional to the square of the object’s speed and its mass.
 Kinetic energy will always be positive.
 But a change in kinetic energy can be negative!

EXAMPLE 1 – Find the indicated value.
 A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have?

 A car has a kinetic energy of 4.32 × 105 J when traveling at a speed of 23 m/s. What is its mass?

 What is the speed of a 0.145 kg baseball if its kinetic energy is 109 J?

HOMEWORK 
Physics  Chapter 5  Lesson 39: WorkKinetic Energy Theorem  Notes 
NOTES
 The WorkKinetic Energy Theorem states that the change in kinetic energy is equivalent to the work done by the object.
Leave space for proof.
 This gives the more useful form of the WorkKinetic Energy Theorem

EXAMPLE 1 – Use the WorkKinetic Energy Theorem to solve the following.
 A student wearing frictionless inline skates on a horizontal surface is pushed by a friend with a constant force of 45 N. How far must the student be pushed, starting from rest, so that her final kinetic energy is 352 J?

 A 90 kg skydiver wants to fall 200 m before opening her parachute. She calculated before her flight that her speed needs to be 62.6 m/s before she pulls her chute. After she opens her chute she reads her wrist speedometer as 5.0 m/s. How much work did the parachute perform on the skydiver?

EXAMPLE 2  Use the WorkKinetic Energy Theorem to solve the following.
 A 10.0 kg grocery cart is pushed 12.0 m along an aisle by a shopper who exerts a constant horizontal force of 40.0 N. If all frictional forces are neglected and the cart starts from rest, what is the grocery cart’s final speed?

 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.

 A 2.0 × 103 kg car accelerates from rest under the actions of two forces. One is a forward force of 1140 N provided by traction between the wheels and the road. The other is a 950 N resistive force due to various frictional forces. Determine how far the car must travel for its speed to reach 2.0 m/s.

HOMEWORK 
Physics  Chapter 5  Lesson 40: Potential Energy  Notes 
LEARNING TARGET JOURNAL
 What is potential energy?
 Name as many different types of potential energy as you can.

NOTES
 Potential energy is energy stored within an object relative to a give zero level.
 We will use U for the variable for potential energy, or understood energy.
 Gravitational potential energy
 Elastic potential energy
 Gravitational potential energy is stored energy due to an object’s position relative to the surface of the Earth.
GPE is proportional to both the mass and height of the object, as well as the strength of the gravity.
 Gravitational potential energy will most often be positive.
 Disregard the direction of gravity to be negative and use .
 The height is measured straight down to the ground, regardless of the path taken to reach that position.
EPE is proportional to the square of the displacement of the spring.
 where x represents the amount the spring has been compressed or stretched relative to its natural length.
 and k represents the spring constant, or force constant, of the spring indicating the strength of the spring
 The units for the spring constant are .
 Elastic potential energy will always be positive.

EXAMPLE 1 – Find the indicated measure using gravitational potential energy.
 A box has a mass of 5.8 kg. The box is lifted from the garage floor and placed on a shelf. If the box gains 145 J of Potential Energy, how high is the shelf?

 A man climbs on to a wall that is 3.6 m high and gains 2268 J of potential energy. What is the mass of the man?

EXAMPLE 2 – Find the indicated measure using elastic potential energy.
 Determine how much energy a spring with a spring constant of 15 N/m stores if it is stretched by 1.6 m.

 A spring with a force constant of 5.2 N/m has a relaxed length of 2.45 m. When a mass is attached to the end of the spring and allowed to come to rest, the vertical length of the spring is 3.57 m. Calculate the elastic potential energy stored in the spring.

EXAMPLE 3  A 2.00 kg ball is attached to a ceiling by a 1.00 m long string. The height of the room is 3.00 m. What is the gravitational potential energy associated with the ball relative to each of the following?
 The floor

 The ceiling

 A point at the same elevation as the ball.

EXAMPLE 4  A 40.0 kg child is in a swing that is attached to ropes 1.50 m long. Find the gravitational potential energy associated with the child relative to the child’s lowest position under the following conditions:
 when the ropes are horizontal

 when the ropes make a 30.0° angle with the vertical

 at the bottom of the circular arc

HOMEWORK 
LEARNING TARGET JOURNAL
Why does Dr. Walter Lewin not want to push the pendulum bob when he first drops it?

NOTES
 That means the amount of total energy will never change, just the type(s) of energy.
This yields the following conservation equation:
 Identify the form(s) of energy before the event.
 Identify the form(s) of energy after the event.
 Set the two expressions from above equal to each other and solve.
 YOU WON’T USE ALL TERMS OF THE EQUATION EVERY TIME!

EXAMPLE 1 – A 75.5 kg 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.

 Find the diver’s speed just before striking the water.

EXAMPLE 2 – Solve the following.
 A child and sled with a combined mass of 50.0 kg slide down a frictionless hill that is 7.34 m high. If the sled starts from rest, what is its speed at the bottom of the hill?

 A bird is flying with a speed of 18.0 m/s over water when it accidentally drops a 2.00 kg fish. If the altitude of the bird is 5.40 m and friction is disregarded, what is the speed of the fish when it hits the water?

 An Olympic runner leaps 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?

HOMEWORK 
Physics  Chapter 5  Lesson 42: Conservation of Energy with Friction  Notes 
LEARNING TARGET JOURNAL
 Why must the first hill of a roller coaster be the largest?
 What factors influence the height of the subsequent hills and loopdeloops on a roller coaster?

NOTES
 Resistive forces like friction use the mechanical energy to do work.
 Work on the initial side (left side) of the equation would come from an applied force.
 Work on the final side (right side) of the equation is a result of friction or air resistance.

EXAMPLE 1 – Solve the following.
 A large airfilled 0.100kg plastic ball is thrown up into the air with an initial speed of 10.0 m/s. At a height of 3.00 m, the ball’s speed is 3.00 m/s. What amount of its original energy has been lost to air resistance?

 A child riding a bicycle has a total mass of 40.0 kg. The child approaches the top of a hill that is 10.0 m high and 100.0 m long at 5.0 m/s. If the force of friction between the bicycle and the hill is 20.0 N, what is the child’s velocity at the bottom of the hill?

HOMEWORK 
Physics  Chapter 5  Lesson 43: Force vs Position Graphs  Notes 
NOTES
 A Force vs Position Graph plots a varying force at every given position during the displacement.
 The area under a Force vs Position Graph calculates the work being done.
 The slope of a Force vs Position Graph gives the units of the spring constant, or force constant, for the displacement.

EXAMPLE 1 – Use the Force v Displacement Graph at the right to answer the following.
 Find the work done during the first 1.5 meters.

 Find the work done during from 1.5 to 3.0 meters.

 Find the net work done during the event.

 Find the force constant at work from 2 meters to 3 meters.

 Describe an event that could have created this graph.

HOMEWORK 
Physics  Chapter 5  Lesson 44: Power  Notes 
NOTES
EXAMPLE 1 – Find the indicated value.
 How long does it take a 19 kW steam engine to do 6.8 × 107 J of work?

 A horizontal force of 150 N is used to push a 40.0 kg packing crate a distance of 6.00 m on a rough horizontal surface. What average power is needed to move the crate in 9.00 s?

 A 1.00 x 103 kg sports car accelerates from rest to 25.0 m/s in 7.50 s. What is the average power output of the automobile engine?

 A 700 N marine in basic training climbs a 10.0 m vertical rope at a constant speed of 8.00 s. What is his power output?

HOMEWORK 
Physics  Chapter 5  Lesson 45: Instantaneous vs Average Power  Notes 
LEARNING TARGET JOURNAL
 If weightlifter A can lift the same amount of weight in less time than weightlifter B, which weightlifter is more powerful? Explain.
 If weightlifter A can lift more weight in the same amount of time than weightlifter B, which weightlifter is more powerful? Explain.

NOTES
 Because the time interval only accounts for an initial and final amount of work performed, our measurement is an average power.
Leave space for proof.
 Instantaneous power is the product of the net force and the instantaneous velocity of the object.

EXAMPLE 1 – Solve for the following.
 An engine moves a boat through the water at a constant speed of 15 m/s. The engine must exert a force of 6.0 kN to balance the force that the water exerts against the hull. What power does the engine develop?

 A car is driven at a constant speed of 76 km/h down a road. The car’s engine delivers 48 kW of power. Calculate the average force that is resisting the motion of the car.

HOMEWORK 