I. Energy & Work

A radiometer shows that light is energy by converting light energy into heat energy and then into movement (kinetic energy)

I. Energy – - Vector? Scalar?

II. Work

A. Defined –

Challenge Question: Two people exert a 10 Newton force on a block for 2 meters. One person exerts her force at a 50-degree angle. (frictionless)

B. Equation:

$\theta$ - the angle between the and

C. Positive and Negative Work

Work is negative when

Work is positive when

Work is 0 when

Examples of negative work

Ex) A 5.0 N force pushes a box 3.0 m North and then 4.0 m east. Find the work done.

Quick Check

3 questions on I. Energy & Work — pick an answer to check yourself.

1. A 10 N force pulls a box 4.0 m along the floor; the force is at 60° to the displacement. How much work does it do?

A) 40 JB) 20 JC) 35 JD) 0 J

2. A waiter carries a tray horizontally across a room at constant velocity. How much work does his upward force on the tray do?

A) Positive, since he holds it upB) Negative, since gravity pulls downC) It equals the tray's weight times the distanceD) Zero, since the force is perpendicular to the displacement

3. A 5.0 N force pushes a box 3.0 m north, then 4.0 m east, always in the direction of motion. Total work done?

A) 35 JB) 25 JC) 15 JD) 20 J

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II. Work Case Studies

W = Fd

Ex 1) Object pushed at an angle, f≠0, Mass m, Force F, μ, Fn

Find the Net Work done on the mower in terms of the variables given

Ex 2) Find the minimum work needed to push a 950 kg car 810 m up a 9.0 deg incline,

W ork is minimal when

a) no friction

b) friction μk = 0.25

Ex 3) Textbook p. 162) 8

330 kg piano, slides down 3.6 m, 28° incline / uk = .40. Man prevents the piano from accelerating down the incline

(a) Force exerted by the man?

b) Work done by a man on the piano?

c) Work done by friction?

d) Work done by the force of gravity?

(e) Net work done on the piano?

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D. Finding Work using a F vs. d plot

Ex 4)

W =

Ex 5) p. 162) 14 a) Sketch the plot described below

b) Find the work

Quick Check

3 questions on II. Work Case Studies — pick an answer to check yourself.

1. On a force vs. displacement graph, the force rises steadily from 0 N to 5.0 N over 6.0 m. How much work is done?

A) 30 JB) 1.2 JC) 15 JD) 11 J

2. What is the minimum work needed to push a 100 kg cart up a 5.0 m frictionless ramp to a height of 2.0 m? (g = 9.8 m/s²)

A) About 4.9 × 10³ JB) About 2.0 × 10³ JC) 200 JD) About 9.8 × 10² J

3. A man holds back a piano so it slides down a ramp at constant velocity. What is the net work done on the piano?

A) Positive, because gravity does the most workB) Negative, because friction and the man oppose motionC) Equal to the work done by gravityD) Zero, because its kinetic energy does not change

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III. Potential Energy

Potential Energy – Stored energy due to or

Gravitational PE

Equation - or

W is + when

W is - when

Ex 1) A 1.60 m person lifts a 2.10 kg book from the ground to 2.20 m above the ground. a) How much work was done lifting the book?

Elastic PE

Equation: PE = Fx     F – Average Force     x – stretch/compression

Ideal Spring – F and stretch

Spring Constant k = F/x

Ex 2) A spring with k = 53 N/m hangs vertically on a ruler. The end of the spring is next to the 15 cm mark on the ruler. If a 2.5 kg mass is now attached to the end of the spring, where will the end of the spring line up with the ruler marks?

PE = [F/2]x = 1/2kx²

Ex) Plot of PE vs x?

Elastic P.E./Plot

PE = of the triangle under F vs x graph

Ex 3) Find the Elastic PE when the spring is stretched 6 m

Ex 4) If 15. Joules of energy are stored in the stretched spring, what is the value of the spring constant?

Ex 5) A 1200 kg car rolling on a horizontal surface has a v = 65 km/hr when it strikes a horizontal coiled spring and is brought to rest at a distance of 2.2 m. What is the spring constant of the spring?

Quick Check

3 questions on III. Potential Energy — pick an answer to check yourself.

1. How much work is done lifting a 2.0 kg book 1.5 m straight up at constant speed? (g = 9.8 m/s²)

A) 3.0 JB) 29 JC) 2.9 JD) 13 J

2. An ideal spring's stretch is doubled. Its stored elastic potential energy…

A) doublesB) halvesC) stays the sameD) quadruples

3. A spring stores 15 J when stretched 1.0 m from its natural length. What is its spring constant?

A) 30 N/mB) 15 N/mC) 7.5 N/mD) 60 N/m

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IV. Kinetic Energy
& Power

I. Kinetic Energy

I. Kinetic Energy – Energy of

A. KE = Work to stop or Work to get an object from rest to a certain speed

Derive KE Equation

KE = W = Fd Where Vf = 0

KE = (ma)d

Equation -

B. KE/m relationship     KE/v relationship

Plot shape

C. When Work is done on an object KE is changed:

W = ΔKE

When is the Work done on an object Negative?

When is the Work done on an object Positive?

D. Scalar or Vector?

Ex 1) A softball having a mass of .25 kg is pitched at 95 km/hr. When it reaches the plate, the ball slows down by 10%. Neglecting gravity, estimate the average force of friction if the distance to the plate = 15 m

Ex 2) baseball (m = 140 g) traveling 32 m/s caught by a glove and moving the glove back 25 cm. Average F of the ball on the glove?

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Power

II. Power - the rate of doing or expending

A. Equation P = W/t = =

B. Scalar or Vector?

C. Units

Ex 3) 1440 kg car accelerates from rest to 95 km/hr in 7.4 sec. What average power is used?

Ex 4) A 95 kg football player runs upstairs in 66 s. The stairs are 140 m long at an angle of 32° (constant V)

Her power output vertically is

Ex 5) 1200 kg car has a max. power output of 120 hp. How steep a hill can it climb at a constant speed of 75 km/hr if the frictional force is 650 N?

1 HorsePower = 746 Watts

Quick Check

3 questions on IV. Kinetic Energy & Power — pick an answer to check yourself.

1. If an object's speed doubles, its kinetic energy…

A) doublesB) stays the sameC) quadruplesD) halves

2. A 50. kg student climbs stairs, rising 4.0 m vertically in 5.0 s at constant speed. What is her average power? (g = 9.8 m/s²)

A) 40 WB) 1960 WC) 98 WD) 390 W

3. A glove catches a baseball and brings it to rest. The work done by the glove on the ball is…

A) negative, because the force opposes the ball's displacement and KE decreasesB) positive, because the glove pushes on the ballC) zero, because the ball ends at restD) positive, because work is always positive

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V. Conservation
of Energy

I. Law of Conservation of Energy - unless is done on or by a system, its total mechanical energy does not change.

Ex 1) Fill in the missing energies

Ignore friction

Ex 2) a) If friction is negligible when the RED ball is released, how high will it rise?

A   B   C   D   Cannot be determined

b) If friction is negligible when the BLUE ball is released, how high will it rise?

A   B   C   D   Cannot be determined

If KE at A is 0 J, find the KE and PE at each point (frictionless)

Ex 3) Fill out the chart below

Ex 4) What physics law explains why the cart will not reach point H and I?

Ex 5) If PE at A = 10. J, KE = 0, and PE at C = 3.0 J, find the PE and KE at all other points

Ex 6) 1.0 kg pendulum swings to a height of .20 m above its lowest point. K.E. of the pendulum at the lowest point?

Ex 7) 5.00-kg cart at the foot of a hill 10.0 m high. For the cart to reach the top of the hill, what is the minimum KE of the cart in the position shown?

Ex 8) Find the height of the pendulum in terms of θ and L (pendulum length)

Quick Check

3 questions on V. Conservation of Energy — pick an answer to check yourself.

1. A 1.0 kg pendulum swings up to 0.20 m above its lowest point. What is its kinetic energy at the lowest point? (g = 9.8 m/s²)

A) 0.20 JB) 9.8 JC) 1.96 JD) 19.6 J

2. A frictionless coaster starts from rest with 100 J of potential energy. At a lower point its PE is 40 J. What is its KE there?

A) 60 JB) 40 JC) 100 JD) 140 J

3. A ball is released from rest at height h on a frictionless U-shaped track. How high will it rise on the other side?

A) Higher than h, because it gains speed at the bottomB) Lower than hC) Twice hD) Exactly h

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VI. Advanced COE
& Work

Relationship: $W = \Delta KE + \Delta PE + W_f$

1. Neglecting air resistance, how high will a 0.325-kilogram rock go if thrown straight up by someone who does 115 J of work on it?

2. A hammerhead with a mass of 2.0 kilogram is allowed to fall onto a nail from a height of 0.40 meters. What is the maximum amount of work it could do on the nail?

3. A 1,200-kilogram car traveling at 110 kilometers per hour (30.55 m/s) comes to a stop.

a. How much work (negative) was done on the car? Don't solve, just show the equation.

b. Where does the car's kinetic energy go?

4. A baseball (m = 0.140 kilograms) traveling 35 meters per second moves a fielder's glove backward 0.25 meters when the ball is caught and brought to rest. What is the average force exerted by the ball on the glove?

5. In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy. With what minimum speed must the athlete leave the ground to lift her center of mass 2.10 meters across the bar at 0.70 meters per second?

1.

a. A 5.0-kg block starts at a speed of 10. m/s at the top of a "roller-coaster," as shown above. What is its KE at the top?

b. What is its GPE at the top (relative to the ground)?

c. What is the block's total energy at the top?

2. If the track is entirely frictionless and there is no air resistance, the block will not lose any energy until it reaches the level surface where μ=0.5 and the frictional force "takes away" energy.

a. Find the GPE at point A and then calculate how much of the block's total energy must be in the form of KE. Also, find the speed at point A.

b. Repeat the above for points B, C, and D.

3. After the block exits the loop-the-loop, it encounters a horizontal, rough surface (μ = 0.5) and comes to a stop.

a. How much total energy does the block have just as it exits the loop-the-loop?

b. How much energy does the frictional force "take away" in bringing the block to a stop?

c. How large is the frictional force acting on the block?

d. How far does the block slide before coming to a stop?

1. A 20. kg block, originally at rest, is pulled across a rough surface (μ = 0.10) by a 100. N force angled at 36.87° for 20. m. Find the work done by each of the following forces.

a. Find the work done by the force of friction

b. Find the work done by Force 100. N.

c. Find the total work done by all of the above forces.

d. Find the speed of the block the instant it is 20. meters to the right of its starting position.

2. A 20.-kg block slides across a frictionless floor and then slides up 10. meter along a rough 36.87° incline (μ =0.20) until it comes to a brief stop. What is the initial speed of the block prior to sliding up the incline?

3. A 5.0 kg box is pulled up a rough (μ = 0.10) incline by a force of 50. N for a distance of 20. m. If the speed of the box is 5.0 m/s initially, what is its speed the instant it has traveled the 20. -m up the incline?

Equation

4. A 10.-kg box is released from rest and slides down an 800. cm tall incline and then compresses a spring (k = 50. N/m). What is the maximum spring compression before the box is pushed away?

Note: all surfaces are frictionless except the crosshatched surface where d = 10. m and has a coefficient of friction of 0.10.

5. A 10.-kg box is held against a spring, which is compressed 2.0 m as shown. If the box is moving at 10. m/s when it reaches the top of the incline, what is the spring constant (k)?

Note: all surfaces are frictionless, and the height (H) of the incline is 6.0 meters.

6. The system above is released from rest. The instance the suspended mass has fallen 8.0 meters, the blocks have speeds of 8.0 m/s. ($m_{susp} = 6.0 \, kg$, $m_{table} = 4.0 \, kg$).

a. How much GPE did the suspended mass "lose" the instant the suspended mass has fallen 8 meters?

b. Where did the GPE "lost" go? Note: disregard air resistance

c. What is the KE of each block, the instant the suspended mass has fallen 8 meters?

d. How much energy did the frictional force "take away" from the system (neg. work)?

e. How large is the frictional force?

f. What is the coefficient of friction?

Check Your Understanding

5 quick questions — pick an answer to see if you’re right.

1. A 5.0 N force pushes a box 3.0 m north, then 4.0 m east, always in the direction of motion. How much total work is done?

A) 35 J B) 25 J C) 20 J D) 15 J

2. In W = Fd cos θ, when does a force do zero work on a moving object?

A) When the force is opposite the motion B) When the force is parallel to the motion C) When the force is perpendicular to the displacement D) When the object moves at constant speed

3. A spring stores 15 J of elastic potential energy when stretched 1.0 m. What is its spring constant?

A) 15 N/m B) 30 N/m C) 7.5 N/m D) 60 N/m

4. A 0.20 kg ball moving at 10 m/s is caught, pushing the glove back 0.10 m. What average force does the ball exert on the glove?

A) 10 N B) 20 N C) 200 N D) 100 N

5. A car's speed doubles. What happens to its kinetic energy?

A) It doubles B) It quadruples C) It stays the same D) It is cut in half

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