Lesson #1 – Introducing Energy

Pre-Lesson Notes

Unit: Energy Read textbook 7.4, 7.5, 7.6 Homework: pg 160 Q1-2, pg 163 Q1-6 and worksheet #3 (attached) Date: Concept: What is Energy

Definitions:Energy

Types of Energy

Equations:Gravitational Potential Energy equation:

Kinetic Potential Energy equation:

1

A.

B.

v

v

Moment A Moment BEnergy is inputted into the

system by your hand

EkEg EkEg

SPH3U: Introducing Energy!

Energy is never created or destroyed; it just moves around and is stored in various ways. This investigation introduces you to energy conservation and its connection to the concept of work.

Here are some basic definitions, phrased informally: Kinetic energy : The energy stored in the motion of an object. The heavier or faster something is, the

more kinetic energy it has. Thus, Ek is basically the energy due to an object’s speed, v. Gravitational potential energy : The energy stored in an object because it has been lifted. The energy is

“potential” because it has the potential to turn into kinetic energy—for instance, if the object gets dropped. The heavier or higher an object is, the more potential energy is stored up. So Eg is basically energy due to an object’s height, h.

A: Work and Gravitational Potential Energy

1. A student holds a book of mass m in her hand and raises the book vertically at constant speed through a displacement Δh. Sketch a free-body diagram for the book. Is the force exerted by the student on the book greater than, less than, or equal to m·g? Explain briefly.

2. Suppose the student uses 15 units of energy while lifting the book from position A to position B. Note that the book always has the constant speed, v.

(a) What quantities of energy change while the student lifts the book? Explain.

(b) By how much did the potential energy of the book change? Explain.

(c) Complete the energy storage diagram for the book. Why is the total energy of the system changing?

The energy of a system can change due to a force acting on it during a displacement. The energy change of the system due to a force is called work. When the force, F, points in the same direction as the object’s displacement, ∆d, the amount of work is positive and is given by W = Fa∙∆d.

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Recorder: __________________Manager: __________________Speaker: _________________

0 1 2 3 4 5

FBD

Moment A Moment BBall falls

down toward

the earth

EkEg EkEg

3. Now let’s study this system again using the idea of work. (a) Use the definition of work to determine the amount of work the student does in raising the book through a vertical displacement, or height. Express your answer using the symbols m, g, and Δh. (Hint: according to your FBD in #1 above, what is your Fa equal to?)

(b) Explain how you could use the result from question A#3a to figure out how much the potential energy has increased.

The gravitational potential energy of an object of mass, m, located at a vertical position, h, above a reference position is given by the expression, Eg =mgh. The reference position is a vertical position that we choose to help us compare gravitational potential energies. At the reference position, the gravitational potential energy is chosen to equal zero. Note that the units for work and gravitational potential energy are Nm. By definition, 1 Nm = 1 J, or one joule of energy. In fundamental units, 1 J = 1 kgm2/s2. In order to get an answer in joules, you must use units of kg, m, and s in your calculations!

1. What does it mean when we say that a book has, for example, 27 J of gravitational potential energy relative to a table (the reference position)?

When we say that the “book has” 27 J of potential energy we always mean the earth-book system. Energy is stored gravitationally due to an interaction between two objects, the book and earth. The book doesn’t really “have” the energy.

B: The Ball Drop and Kinetic EnergyNext, you will drop a tennis ball from a height of your choice (between 1 and 2 m) and examine the energy changes.

1. Draw a diagram of a ball falling and indicate two moments in time A and B at the start and end of its trip down (just before impact - JBI!) Draw a dashed horizontal line at the bottom which represents your vertical reference position. Label this “h = 0”. Indicate the starting height you chose.

2. Calculate how much gravitational potential energy the ball initially has with respect to the reference line. What measurement do you need to make? (use m = 57 g)

3. Draw an energy storage bar graph for the earth-ball system from moments A to B.

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4. Exactly how much kinetic energy do you predict the ball will have just before it reaches the ground? Explain.

The kinetic energy of an object is the energy stored in the motion of the object. The more mass or the more speed the object has, the greater its kinetic energy. This is represented by the expression, Ek = ½mv2. Energy is measured in units of joules (J) and is a scalar quantity since energy does not have a direction. m must be in kg and v must be in m/s.

5. Use the new equation for kinetic energy to determine the speed of the ball just before it hits the ground.

6. If you have time, u se the motion detector set up by your teacher to measure the speed of the ball just before it hits the ground. How do the two results compare?

Gravitational potential and kinetic energy are two examples of mechanical energy. When the total mechanical energy of a system remains the same we say that the mechanical energy is conserved. Mechanical energy will be conserved as long as there are no external forces acting on the system and no frictional forces. If mechanical energy is conserved, we can write an energy conservation equation which equates the sum of kinetic and potential energies at two moments in time: Emech = EkA + EgA = EkB + EgB

7. Keeping in mind the experimental errors, was mechanical energy conserved during the drop of the ball? Explain.

8. Write down the energy conservation equation for ball drop example. If a quantity equals zero, leave it out.

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Lesson #2 – Doing work or hardly working?

Pre-Lesson Notes

Unit: Energy 7.1Homework: pg 151 Q1-4 and worksheet #2 (attached) Date: Concept: What is work

Definitions:

Work

Joule

Equations:Work Equation:

Explanation:

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SPH3U: Doing work?

A: Working Hard or Hardly Working?In this section we’ll clarify the meaning of work. Remember: W = F∆d

1. A student pushes hard enough on a wall that she breaks a sweat. The wall, however, does not move; and you can neglect the tiny amount it compresses. Does the student do any work on the wall? Answer using:

a. your intuition.

b. the physics definition of work.

Apparently, some reconciliation is needed. We’ll lead you through it.

2. In this scenario, does the student give the wall any kinetic or potential energy?

3. Does the student expend energy, i.e., use up chemical energy stored in her body?

4. If the energy “spent” by the student doesn’t go into the wall’s mechanical energy, where does it go? Is it just gone, or is it transformed into something else? Hint: Why does your body produce sweat in a situation like this?

5. Intuitively, when you push on a wall, are you doing useful work or are you “wasting energy”?

6. A student says:“In everyday life, ‘doing work’ means the same thing as ‘expending energy.’ But in physics, work corresponds more closely to the intuitive idea of useful work, work that accomplishes something, as opposed to just wasting energy. That’s why it’s possible to expend energy without doing work in the physics sense.”In what ways do you agree or disagree with the student’s analysis?

The net work is the sum of all the work being done on the system. When the net work is non-zero, the kinetic energy of a system will change. If the net work is positive, the system gains kinetic energy. If the net work is negative, the system loses kinetic energy. This is called the kinetic energy - net work theorem and is represented by the expression: Wnet =EkB – EkA = Ek .

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A BBall1

Ball2

Lesson 3: Gravitational Potential Energy

We have had a brief introduction to energy stored due to an object’s position, that is, gravitational potential energy. Today we will explore this idea in depth.

A: The Ramp Race - PredictionsYour teacher has two tracks set up at the front of the class. One track has a steep incline and the other a more gradual incline. Both start at the same height and end at the same height. Friction is very small and can be neglected.

1. Use energy transfers to describe what will happen as a ball travels down an incline.

2. How will the speeds of each ball compare when they reach the bottom of their ramps? Why?

3. Each ball travels roughly the same distance along the tracks between points A and B. Which one do you think will reach the end of the tracks first? Use energy arguments to support your prediction.

B: The Race!1. Record your observations of the motion of the balls when they are released on the tracks at the same time.

2. Record your observations of the speeds of the balls when they reach the end of the track.

3. Marie says, “I’m not sure why the speeds are the same at point B. Ball 1 gains energy all the way along a much longer incline. Surely more work is done on it because of the greater length of the incline. Ball 1 should be faster.” Based on your observations and understanding of energy, help Marie understand.

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Recorder: __________________Manager: __________________Speaker: _________________

0 1 2 3 4 5

EgA =

EgB =

Eg =

EgA =

EgB =

Eg =

4. Albert says, “I don’t understand why ball 2 wins the race. They both end up traveling roughly the same distance and ball 2 even accelerates for less time!” Based on your observations and understanding of energy, help Albert understand.

5. According to your observations, how do the kinetic energies of the two balls compare at point B? Where did this energy come from?

6. The distance the balls travel along each incline is different, but there is an important similarity. Compare the horizontal displacement of each ball along its incline (you may need to make measurements). Compare the vertical displacement of each ball along its incline. Illustrate this with vectors on the diagram on the previous page. Which displacement will help determine the change in gravitational potential energy? Also, calculate the expected speed of ball 2 at the bottom.

The amount of energy stored in, or returned from gravity does not depend on the path taken by the object. It only depends on the object’s change in vertical position (displacement). The property is called path independence – any path between the same vertical positions will give the same results. This is a result of the fact that gravity does no work on an object during any kind of horizontal motion.

C: The Vertical Reference PositionWhen making calculations involving gravitational energy, we must choose a vertical reference line from which we measure the vertical position of the object. What effect does this choice have on the results of our calculations? Let’s see! In the following work, if there are any quantities you need to know, make a measurement of the equipment at the front of the room.

Vertical positions above the reference line have positive values, while vertical positions below the reference line have negative values. This is our energy-position sign convention.

Using the measurements from the ramp demo in the previous 2 sections, answer the following questions:

1. In the diagram to the right, draw and label the vertical reference line, h = 0 at the bottom level of the track. What is the gravitational potential energy of the ball at positions A and B?

2. In the diagram to the right, draw and label the vertical reference line h = 0 at the top level of the track. What is the gravitational potential energy of the ball at positions A and B? Remember, we need to consider the new h here as negative.

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3. As the ball rolls down the track, there is a transfer of energy stored in gravity to energy stored in motion. Draw a vector representing the vertical displacement of the ball in each diagram. How do these two vectors compare?

4. How does the change in gravitational potential energy, Eg, compare according to the two diagrams? How much kinetic energy will the ball gain according to each diagram?

Only changes in gravitational potential energy have a physical meaning. The exact value of the GPE at one position does not have a physical meaning. That is why we can set any vertical position as the h = 0 reference line. The vertical displacement of the object does not depend on the choice of reference line and therefore the change in GPE does not depend on it either. So it is not significant if an object has a negative GPE.

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Lesson # 4 – Conservation of Energy – Rollercoasters!

Pre-Lesson Notes

Unit: Energy Read textbook 7.7 Homework: pg 168 Q1-3 and worksheet #1 (attached) Date: Concept: What is Energy

Definitions:Energy

Types of Energy

Equations:Gravitational Potential Energy equation:

Kinetic Potential Energy equation:

Work Energy Theorem:

Conservation of Energy Equation:

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Moment B

EkEg EkEg

Equation

Moment B

EkEg EkEg Ediss

Equation

Moment A

Moment B

Equation

Moment A

SPH3U: The Conservation of Energy – Roller Coasters!

A: The Behemoth A rollercoaster at Canada’s Wonderland is called “The Behemoth” due to its 70.1 m tall starting hill. Assume the train is essentially at rest when it reaches the top of the first hill. We will compare the energy at two moments in time: A = the top of the first hill and B = ground level after the first hill.

1. Draw an energy bar graph for the train. Write down the energy conservation equation.

2.Use the energy conservation equation

to find the speed of the rollercoaster at moment B (& convert to km/h.)

3. The official statistics from the ride’s website give the speed after the first drop as 125 km/h. What do you suppose accounts for the difference with our calculation?

4. Draw a new energy storage bar graph for the train and its surroundings. Write down a new energy conservation equation. Use the symbol Ediss for the energy dissipated (lost) due to friction.

5. Use the train mass, mt = 2.7 x 103 kg to determine the energy dissipated on the first hill. (Hint: use the difference between the energy at the top and the actual energy at the bottom, using the actual speed -- in m/s.)

The dissipated energy is stored in heat, sound and vibrations. Energy stored in these forms are not mechanical forms of energy since it is very difficult to transfer energy stored this way back into kinetic or potential energy.

B: The Bluevale FlyerRumour has it that a rollercoaster is going to be built in the Bluevale field. Plans leaked to the media show a likely design. The train starts from rest at point A. For all our calculations, we will assume that the energy lost to friction is negligible.

1. Point B is located partway down the first hill. Complete the diagrams and determine the rollercoaster’s speed at that moment in time.

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Moment A The sum of all E’s before equals the sum of all E’s after…

A

B

∙∙

Moment D

EkEg EkEg

Equation

Moment ____

2. Point D is the top of the loop-de-loop and is located 70 m above the ground. Complete the diagrams and determine the rollercoaster’s speed at that moment in time. (Hint: We can usually create and solve our equation by comparing Etot at 2 different points. The 2nd point is D. Does it matter which point is 1st?)

The loop-de-loop involves some very complicated physics, the details of

which are much beyond high school physics. Yet using energy techniques, we did not have to consider those complications at all!

When the mechanical energy of a system is conserved, we can relate the total mechanical energy at one moment in time to that at any other moment without having to consider the intermediate motion – no matter how complex.

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A (top of swing)

EkEg EkEg EkEg EkEg

A (top of hill) B (bottom)Car coasts downhill

unassisted

EkEg EkEg

B (ground) C (top of small hill)Car coasts up smaller

hill unassisted

EkEg EkEg A (coasting) B (stopped)

Car gradually comes to

a stop

Lesson #5: The Conservation of Energy – Cars

A: Pendulum practice

Before considering cars, let’s first practice these energy bar diagrams with something fairly simple like a pendulum. Complete these diagrams. Let’s call the lowest point of the swing h = 0. Keep in mind that a pendulum stops for an instant at the top of its swing.

A student says: “Ya, this looks pretty good, but

a

pendulum eventually comes to a stop. So shouldn’t our A and D diagrams be a little different from each other?” Do you agree or disagree?

Is there any way you can think of to change the diagrams so that they make perfect sense and truly show the conservation of energy?

Let’s now practice some energy bar diagrams for simple situations with cars.

B: Regular gas guzzlers

1. A car is coasting at low speed on a flat road and then heads down a steeply inclined hill to reach another flat road at the bottom with a higher speed even though the driver didn’t push on the gas pedal the entire time. Complete a rough energy storage bar diagram for this car:

2. Without slowing much on the way, the same car approaches an uphill incline, about half as high as the other hill. Complete another set of diagrams for this car as it goes up this smaller hill:(a) How will the speed of the car

compare at spots A, B and C?

3. Now the car is on a flat road going a moderate speed and the driver sees a red light ahead. They slow the car gradually by braking until they come to

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B (bottom) C (part way up) D (top of swing)

B (going fast)Car

speeds up from rest

Ek Eg E E

Ek Eg E E

a complete stop. Let’s say h = 0. Complete yet another diagram. We need to start considering more than just Ek and Eg now, so let’s make room for other mystery energy forms.

(a) Since the height and the speed are both zero at the red light (B), then what values do we expect for kinetic and gravitation energy?

A car gets its energy from chemical energy in the fuel tank. Let’s label it on the above diagram as E chem. It doesn’t really change, from A to B, does it?

If the Ek went down but the Eg and the Echem stayed the same, a fourth form of energy must have increased. They say you shouldn’t “ride the brakes” when you go down a big hill, since it can melt your brake pads or even catch them on fire! This is a clue that the energy must have gone into heat. Let’s label it above as Eheat. Like Eg, it is relative; what’s important is how much it changed. So it’s ok to show some Eheat in diagram A if you want, but you have to make it much higher in diagram B since the brake pads would have heated up a lot to dissipate the energy the car had (or if the car skidded to a stop, the road and the tires would heat up a lot!)

4. How will the car get energy again to get up to speed when the light turns green?

(a) Show this on one more energy bar diagram. Do this one in pencil, just in case, since adjustments may be needed after the next question.

(If we want to keep it real here to some extent, keep in mind that internal combustion engines are horribly inefficient. Most cars convert only about 25% of chemical energy into kinetic energy; that is, about 75% of the energy you get from “burning” gasoline goes to useless, problematic heat energy that does no useful work. That’s why cars need radiators to get rid of all this troublesome heat!)

(b) With the bad efficiency in mind, let’s try to add some numbers and put a scale on the diagrams in (a) above. Let’s say you have 80 mL of gas left in your tank only. This is worth about 2 million Joules of chemical energy (or 2 MJ). So you start your car from rest, with the engine cool (we can say Eheat = 0). Calculate how much kinetic energy your 1200 kg car will have after getting up to a speed of 25 m/s.

(c) Since only ¼ of the energy went to your Ek, then ¾ went to Eheat. Multiply your answer in (b) by 3, and this would then be the amount that went to heat. Show your calculations here:

Eheat = ΔEchem = Ek + Eheat =

(d) Add the appropriate scale to your energy diagram above.

C: Hybrid cars

Similar to regular cars, hybrid cars have gasoline engines (often smaller ones) but they also have electric motors and a lot of extra batteries. Batteries are a form of chemical energy, but to distinguish this from fossil fuel E chem,

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A (at rest)

A (top of hill) B (bottom)Hybrid coasts

downhill unassisted, but

doesn’t speed up.

Ek Eg Eheat Echem Ebatt

Ek Eg Eheat Echem Ebatt

A (coasting) B (stopped)Car

gradually comes to

a stop

Ek Eg Eheat Echem Ebatt

Ek Eg Eheat Echem Ebatt

let’s call battery energy Ebatt. When a hybrid goes downhill or when it slows down, the motion of the car is used to spin-up the electric motor which acts as a generator to charge the batteries, in an attempt to save that kinetic energy in a different form so that it can be used again. (Most hybrid cars don’t need to be plugged in.)

1. A hybrid car is coasting at low speed on a flat road and then heads down a steeply inclined hill to reach another flat road at the bottom. Unlike the last time that we considered this scenario, this driver wants to maintain a constant speed. Complete a rough energy storage bar diagram for this car. If you’re unsure how it will look, the questions below may give you some hints. Fuel (Echem) is not used, nor is it gained of course.(a) With a regular car, it starts with a lot of Eg at the top of the hill. This converted to what kind of energy

in section B, question 1?

(b) This time Eg went down again, yet the car didn’t speed up, that is, Ek stayed constant. Where did this energy go?

Although battery technology has come a long way in our lifetime, keep in mind that it has a long way to go still. One reason it took a long time for hybrid cars to become mainstream, is that a lot of the energy is lost on its way to charging the battery. It’s unfortunately not remotely close to 100% of energy transfer to the batteries. For example, the wires heat up, so that’s energy lost to heat again. But recovering even a fraction of the kinetic energy can be worth it, saving significant amounts of energy, fuel, and carbon emissions.

2. Now the hybrid is on a flat road going a moderate speed and the driver sees a red light ahead. They slow the car gradually by “braking”, thus charging the batteries, until they come to a complete stop. Let’s say h = 0. Complete another E bar diagram. (Remember: since the height and the speed are both zero at the red light (B), then we know that Ek

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A (stopped still) B (going fast)Car speeds

up from rest

Hint: if Eheat goes up, a little Echem must be used-up (go down) to

compensate.

Ek Eg Eheat Echem Ebatt

Ek Eg Eheat Echem Ebatt

A (medium speed)

Ek Eg Eheat Echem

Ek Eg Eheat Echem

Ek Eg Eheat Echem

A (medium speed)

Ek Eg Eheat Echem Ebatt

Ek Eg Eheat Echem Ebatt

Ek Eg Eheat Echem Ebatt

C (back up to speed)B (stopped)

and Eg are both zero too.) You can be somewhat realistic here and show that some of the energy was “lost” to heat.

3. Green light, go! What happens when you get the hybrid back up to speed from rest? Here too, a little energy is probably lost to heat. Fill in the diagrams:

(FYI: you may be interested to look up “KERS” online. It’s a cool system to store the kinetic energy in a spinning flywheel instead of a battery. Apparently this type of mechanical system is much more efficient than using a battery.)

D: Summary comparison

Summarize here to compare a regular car to a hybrid. Let’s keep it simple: no hills, so Eg will always be zero. Start with only a little heat energy for both cars.

1. Normal Car:

2. Hybrid Car:

Remember that when the normal car stopped, it couldn’t store any of the kinetic energy that it had, but the hybrid can use that energy to charge the battery, so it’s not lost. Generating electrical energy for the batteries this way while slowing a vehicle is sometimes called “regenerative braking”. A hybrid car can then use this stored energy in the batteries to help it get back up to speed without using much gasoline. Thus, overall, we should see in step C, when they are back up to speed, that Echem (gasoline) lowered more for the normal car than for the hybrid. This fuel saving usually saves a driver enough money after a few years to pay for the extra purchase cost of a hybrid car, making hybrid cars a more and more practical and popular choice for consumers. And let’s not forget the bonus of greatly reduced harmful emissions, such as greenhouse gases!

E. Back to simple mechanical energy

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B (stopped) C (back up to speed)

A (ball at bottom) B (ball at max. h)Ball rolls up a hill

Ek Eg Etotal

Ek Eg Etotal

Time to get back to simpler examples, with just two type of energy: Ek and Eg, so that we can begin to make some calculations. Unless otherwise stated, we will assume that virtually no heat is lost in most of our examples. So the total mechanical energy (Ek + Eg) will be constant; the total value will be the same before and after an event.

Consider a 4.0 kg bowling ball going 5.0 m/s on the flat ground. If it rolls up a hill, up to what height will it roll?

1. Calculate Ek now:

2. What is the speed when it reaches its max. h?

3. Consider these points:- Etotal at the bottom is just Ek (h = 0 so Eg = 0)- Etotal at the top is just Eg (stopped so Ek is zero)Thus, Ek (bott.) = Eg (top) !

4. Use this to solve for the max. height! (You may find it helpful to put a scale on your energy bar graph.)

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Lesson #6 – POWER

Pre-Lesson Notes

Unit: Energy Read textbook 7.2 and 7.3 Homework: pg 153 Q1-6, pg 154 Q1-3Date: Concept: What is Power

Definitions:Power

Watt

Equations:

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SPH3U: PowerWinning a race is all about transferring as much energy as possible in the least amount of time. The winner is the most powerful individual.

Power is defined as the ratio of the amount of work done, W, to the time interval, t, that it takes to do the work, giving: P=W/t. The fundamental units for power are joules/second where 1 joule/second equals one watt (W).

A: The Stair Master (Recall: what are the 2 equations we have for work? Write them here: )

Let’s figure out your leg power while travelling up a set of stairs.

1. Describe the energy changes that take place while you go up the stairs at a steady rate (we will assume v = const., roughly).

2. Explain what you would measure in order to determine the work you do while travelling up a set of stairs. Sketch a diagram of this showing all the important quantities. (Hint: either one of the equations you wrote above will work!)

3. To calculate your power, you will need one other piece of information. Explain.

4. Gather the equipment you will need. Travel up a flight of stairs at a quick pace (but don’t run, we don’t want you to fall!) Record your measurements on your diagram.

5. Compute your leg power in watts (W) and horsepower (hp) where 1 hp = 746 W. How does this compare to your favourite car? (2011 Honda Civic DX = 140 hp; Tesla Roadster = 248 hp.)

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Diagram

Moment B

EkEg EkEg

Equation

Moment A

B: Back to the Behemoth!1. The trains on the Behemoth are raised from 10 m above ground at the loading platform to a height of 70.1

m at the top of the first hill in 60 s. The train (including passengers) has a mass of 2700 kg and is lifted at a steady speed. Ignoring frictional losses, how powerful should the motor be to accomplish this task? Complete the energy diagrams below for the earth-train system. In the energy equation, include a term, Wm, for the work done by the motor.

Lesson #7 – Nuclear Energy

Pre-Lesson Notes

Unit: Energy Read textbook 27.1 – 27.4 and 27.6-27.8 Homework: Date: Concept: Nuclear energy

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Definitions:Nuclear Fission

Nuclear Fusion

Chain Reaction

Nuclear Reactors

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WEP Worksheet #1 - Conservation of Energy Problems1. A 4.0 kg block falls 8.0 m from rest. Assuming a conservative system (that is, that no energy is lost to heat) what

speed does it reach?

2. A 6.0kg rock falls from rest, gaining a speed of 8.0 m/s. Assuming a conservative system, how far did it fall?

3. A 2.0 kg ball is thrown upwards at 8.0 m/s. Assuming a conservative system, how far does it rise? (Use energy approach. Check with acceleration approach)

4. A 4.0 kg ball is thrown upwards at l2.0 m/s. Assuming a conservative system, how far must it rise to slow to 4.0 m/s?

5. A 2.0 kg ball is moving at 3.0 m/s. Assuming a conservative system, how fast is it going after falling 20.0 m?

6. A 6.0 kg rock is thrown upward at 12.0 m/s. Assuming a conservative system, how fast is it going after rising 4.0 m?

7. How much work is needed to get a stationary 6.0 kg block moving at 15 m/s? Assume the block is on a horizontal frictionless surface.

8. How much work must be done to increase the speed of a 4.0 kg ball from 3.0 m/s to 9.0 m/s? Assume the motion is horizontal and that the friction is negligible.

9. 80.0 J of work are done on a 3.0 kg ball moving at 4.0 m/s. Assume its height does not change and that there is no friction. What speed does it reach?

10. How much work is needed to raise a 6.0 kg object 14.0 m at constant speed? Assume that friction is negligible.

11. What is the minimum work that must be done to raise a 30.0 kg object from h = 7.0 m to h = 11.0 m?

12. How much work is needed to raise a 6.0 kg object 4.0 m while increasing its speed from 2.0 m/s to 6.0 m/s? Assume that friction is negligible.

13. How much work must be done to increase the speed of a 4.0 kg ball from 3.0 m/s to 7.0 m/s while raising it 3.0 m? Assume that the friction is negligible.

14. How much work is required to push a 168 kg crate 7.0 m at constant speed across a horizontal floor for which the coefficient of friction is 0.40?

15. 800 J of work are done pushing a 40.0 kg crate 6.0 m along a horizontal surface with μ = 0.30. If the crate started at rest, what speed does it reach?

16. A 600 kg crate slides 12 m down a ramp on which the force of friction is 700 N. If the vertical drop is 6.0 m, what speed does the crate reach?

1. 1.3 x 101 m/s 2. 3.3 m 3. 3.3 m 4. h = 6.5 m 5. 20 m/s

6. 8.1 m/s 7. 6.8 x 102 J 8. 1.4 x 102 J 9. 8.3 m/s 10. 8.2 x 102J

11. 1.2 x 103J 12. 3.3 x 102J 13. 2.0 x 102J 14. 4.6 x 103J 15. 2.2 m/s

16. 9.5 m/s

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WEP Worksheet #2 - Work Problems1. A 75 kg boulder rolled off a cliff and fell to the ground below. If the force of gravity did 6.0 x

104 J of work on the boulder, how far did it fall?

2. A student in a physics lab pushed a 0.100 kg cart on an air track over a distance of 10.0 cm, doing 0.0230 J of work. Calculate the acceleration of the cart (hint: since the cart was on an air track, you can assume that there was no friction).

3. With a 3.00 x 102 N force, a mover pushes a heavy box down a hall. If the work done on the box by the mover is 1.90 x 103 J, find the length of the hallway.

4. A 200 kg hammer of a pile driver is lifted 10.0 m at an acceleration of 0.57 m/s2. Calculate the work done on the hammer (a) by using ΔE; and (b) by using Fa and Δd.

5. A large piano is moved 12.0 m across a room. Find the average horizontal force that must be exerted on the piano if the amount of work done is 2.70 x 102 J.

6. A crane lifts a 487 kg beam vertically at a constant velocity. If the crane does 5.20 x 104 J of work on the beam, find the vertical distance that it lifted the beam.

7. A 2.00 x 102 N force acts horizontally on a bowling ball over a displacement of 1.50 m. Calculate the work done on the bowling ball by this force.

8. Ralph pushes an empty train car (of mass 1100 kg) 12.0 m [E] along a horizontal track with a force of 800 N. The forces of friction (bearings, track, air, drag etc.) acting against the car are 740 N. How much work does Ralph do?

9. Erica pushes a 15 kg crate [E] with a force of 200 N. William pushes the crate [W] at 80 [N]. The force of friction between the crate and the floor is 60 N. Initially at rest, the crate moves 3.0 m [E] . How much work does Erica do?

10. Erica pushes a 800 kg crate along the floor with a force of 2000 N [E]. The force of friction from floor acting against the crate is 1800 N. Initially at rest, the crate reaches a speed of 1.5 m/s while it moves 6.0 m [E]. How much work does Erica do?

ANSWERS:1. 82 m2. 2.3 N/kg3. 6.30 m4. 2.1x104 J (both ways!)5. 22.5 N6. 11.0 m7. 300 J8. 9.6 x 103 J [E]9. 6 x 102 J [E]10. 1.2 x 104 J [E]

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WEP Worksheet #3 - EK and Eg 1. In the sport of pole vaulting, the jumper’s centre of mass must clear the pole. Assume that a 59 kg

jumper must raise the centre of mass from 1.1 m off the ground to 4.6 m off the ground. What is the jumper’s gravitational potential energy at the top of the bar relative to where the jumper started to jump?

2. A 485 g book is resting on a desk 62 cm high. Calculate the book’s gravitational potential energy relative to:

a) the desk topb) the floor

3. Rearrange the gravitational potential energy equation to obtain an equation for:a) m b) g c) h

4. The elevation at the base of a ski hill is 350 m above sea level. A ski lift raises a skier (total mass = 72 kg, including equipment) to the top of the hill. If the skier’s gravitational potential energy relative to the base of the hill is 9.2 x 105 J, what is the elevation at the top of the hill?

5. The spiral shaft in a grain auger raises grain from a farmer’s truck into a storage bin. Assume that the auger does 6.2 x105 J of work on a certain amount of grain to raise it 4.2 m from the truck to the top of the bin. What is the total mass of the grain moved? Ignore friction.

6. A fully dressed astronaut, weighing 1.2 x 103 N on Earth, is about to jump down from a space capsule which has just landed safely on Planet X. The drop to the surface of X is 2.8 m and the astronaut’s gravitational potential energy relative to the surface is 1.1 x 103 J.

a) What is the magnitude of the gravitational field strength on Planet X?b) How long does the jump take?c) What is the astronaut’s maximum speed?

7. Calculate the kinetic energy of:a) 7.2 kg shot put that leaves an athlete’s hand during competition at a speed of 12 m/s.b) a 140 kg ostrich (the fastest 2 legged animal on earth!) that runs at 14 m/s

8. Rearrange the kinetic energy equation to solve for:a) m b) v

9. A softball is traveling at a speed of 34 m/s with a kinetic energy of 98 J. What is its mass?

10. A 97 g cup falls from a kitchen shelf and shatters on the ceramic tile floor. Assume that the maximum kinetic energy obtained by the cup is 2.6 J and that air resistance is negligible.

a) What is the cup’s maximum speed?b) What do you suppose happened to the 2.6 J of kinetic energy after the crash?

11. A locomotive train with a power of 2.1 MW in 1 minute travels at a speed of 35 m/s. Determine the mass of the train.

ANSWERS!1. 2.0 x 103 J2. a) 0 J b) 3.0 J

4. 1.7 x 103 m5. 1.5 x 104 kg 6. a) 3.2 N/kg b)1.3 s c) 4.2 m/s7. a) 5.2 x 102 J b) 1.4 x 104 J9. 0.17 kg

10. a) 7.3 m/s11. 2.1 x 105 kg or 210 metric tones (1 tonne = 1000 kg)

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SPH3U: The Conservation of Energy – Bouncing Ball

Complete this activity as a lab in your lab duotang.

Task: Study and analyze the motion and energy transfers in a bouncing ball. Review relationship between d-t, v-t, and a-t graphs. Review and understand kinetic and gravitational potential energy.

Equipment: video camera that can play back frame by frame, accurate measurements on the wall, bouncy ball, students.

Investigation: Using data previously collected for a bouncing ball, we will now analyze the energy relationships of the ball. Prepare a new table on a new page, with the following long vertical columns: Height (m), Grav. Pot. Energy (J), velocity (m/s), Kinetic Energy (J), Total Mech. Energy (J). Weigh the ball to get its mass in kg. Transfer your position values to the Height column and use them to calculate Eg. Transfer you velocity values (converted to m/s) and use them to calculate Ek. Add Eg and Ek to get Etotal.

On a large graph, plot three lines: Eg vs time (not Δt), Ek vs time, and Etotal (mechanical energy) vs time. Take care to choose an appropriate scale that will fit the total energy!

Analysis:

1. Describe what happens to each energy (Eg and Ek) as the ball is on the way down.2. Describe what happens to each energy (Eg and Ek) as the ball is on the way up.3. Describe what happened to the total energy over the ball’s entire trip. Was there a general trend, roughly?4. Give an explanation for any change in the total energy.5. Discuss whether or not energy is conserved in this system.6. Google the phrase “isolated system” and comment whether or not the system in this lab is isolated.7. When the ball is in contact with the ground, both Eg and Ek would be zero or close to zero. This would imply

that the total energy (as seen on your graph) is suddenly zero or close to zero. But then an instant later, the total energy jumps back up. The real total energy should be constant. Thus, during the bounce a different type of energy must increase for a moment. What type of energy could this be? Explain your reasoning.

8. Calculate the % change in total energy from the beginning to the end.

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