Unit 5 Summary

Hello physicists both big and small, it's time again to sum up what we leaners in our current unit. In unit 5 we learned of four key concepts....

1.) Work and Power

2.) Work and Kinetic Energy Relationship

3.) Conservation of Energy

4.) Machines

Unlike our past units, I did not learned an "expectional" amount of formulas, information, and applications to everyday life. Don't get me wrong, we still did learn some, just less than usual. However, as usual I will pour in some questions, use a dash of example problems, and sprinkle it all with my "goofballness" (according to my mother).  Bon Appetite!

Part one: Work and Power

1.) What is the formula for work?

The formula is Work= Force x Distance.

2.) What is work responsible for?

Work is responsible for power.

3.) What is work measure in?

Work is measured in Joules.

4.) What relationship must the force and distance have to have in order for a force to do work on an object.

The force and the distance must be parallel for the force to do work on an object.

5.) If no distance is covered when force is applied, is there work being done?

No, there is no work being done. The force must cause a certain distance to be covered by the object.

6.) What is the formula for power?

The formula is Power = Work/ Time.

7.) What is power measured in?

Power is measured in watts.

8.) How many watts equals one horsepower?

746 watts equals one horsepower.

Examples and Practice Problems 

1.) Your friend just had surgery, but they just bought a new apartment. They need to pack up their stuff and move it across the hall to the new apartment. You pack up a box and push with 200N for 5m. How much work was done?

Here is the picture to use to solve the problem....

Answer......

2.) Oh no! You forgot to do leg day at the gym! So you decide to lift the box using 200N of force. You carry the box using one hand for 10m. How much work was done on the box? (remember that when lifting the box there is work done, but as soon as you start walking...see answer below)

Here is the picture to refer to, to answer the question.....

Answer.....


No work is done on the box! This is because the force and distance aren't parallel. For work to be done, the force and distance must be parallel. They are perpendicular here as he is mixing with the box.



3.) Is there work done here? If so, explain why?


Here is a picture to refer to for the answer....

Answer.....


No, there is no work done here. While the force and distance are parallel, there is no distance covered. There must be a distance covered for work to be done.


4.)  Finally, language class has ended. Mr. Alexander finished grading your test, so you walk upstairs slowly afraid to see your grade. You apply 600N of force going up the stairs which are 4 meters tall. How much work was done here?

Here is the picture to refer to to help you answer the question....

Answer.... (Keep in mind the time)

4.5)  How much power was there? Use the formula you learned about in the questions above to answer the question.



Answer....

5.) Oh no! You spend to long doing a celebration dance, happy you got a 100 on the test and you are late for history on the fourth floor. You grab your text books, which you apply 20 more newtons of force on the stairs. How much work is down now? 

Here is the picture to refer to for the answer....

Answer..... 

5.5.) How much work was done now? Keep in mind the change in work and time 

Answer....

Part two: Work and Kinetic Energy Relationship 

1.) What is the formula for Kinetic energy?

2.) What is the relationship between work and energy?

3.) Where does the word energy come from? How is this related to work? 

The work energy comes from the word "energy" or energy. It is the ability to do work. 

4.) Where does the word Kinetic come from?

It comes from the greek word "Kinema" which means movement or kinetic energy.

Examples and Practice Problems

1.) A car is going 20m/s when the driver slams on he breaks. The car skids 6m to a stop. A while later the same car is going 40m/s on the same pavement and the driver slams on his breaks. How far does the car skid before stopping?

2.) You are lost in the woods! All if silent, then all of a sudden with the glow of the moon shining down on a 20kg wild bear. He is accelerating toward you going from 10m/s to 20m/s in 10s over a course of 100 meters. What is the change in Kinetic energy the crazed bear experiences? How much work was done? How much power does the fiercely fabulous bear do? How much was the force that caused the bear to accelerate?

Change in KE.....

Answer...

Work....

Power....

Force.... 

3.) Why do airbags keep you safe?

4.) Two people each exert 600N of force went up to the top of the Eiffel Tower, which is approximately 100m. One took the stairs and the other took the elevator. Which person did gravity do more work on. (Show work or explain) 

Explanation....

They did the same amount of work because work= force X distance. They both exerted the same force over the same distance. Since the force and distance are the same and parallel, gravity did the same amount of work on each of them. 

Work....  

Part 3: Conservation of Energy 

1.) What is the formula for PE (Potential Energy)? 

The formula is PE = mgh (Mass X Gravity X Height). 

2.) What is the relationship between PE and KE? 

PE= KE at its lowest point. 

3.) What is PE measured in? 

It is measured in Joules. 

4.) Can something be moving and have Potential Energy? If so, provide an example and your reasoning? 

Yes, something can be moving and have potential energy. This is because it is the energy of position and at any position it has height. 

5.) Can something be at rest and have Kinetic Energy? If so, provide an example and your reasoning? 

No, it cannot be at rest and have Kinetic energy. This is because Kinetic energy depends on velocity and when at rest the velocity is zero. 

6.) What does the law of the conservation of energy imply? 

It implies that energy is conserved. Energy can neither be created nor destroyed, but can be changed into another form. 

Examples and Practice Problems

1.) You and a friend decide to drop a 20kg watermelon from a 4m ladder. How much potential energy does the watermelon have? What will the Kinetic Energy be just before it hits the ground? What is the speed that the ball will have just before it hits the ground?

Potential Energy....

Kinetic Energy just before it hits the ground....

Speed.....

2.) You decide to ride the Hulk at Universal in Orlando, Florida. A chain takes you to the top of the hill, but once released you move only due to the laws of physics. Why are you all able to complete the ride on the roller coaster? 

Here is what the roller coaster looks like....

Here is what the coaster looks like with PE and KE labels....

Answer: According to the law of the conservation of physics, energy can neither be created nor destroyed. Instead, it is converted into another form. In this situation, the PE is being converted into KE, but it is always conserved. It is for this reason why we continue to go, whether or not the next hill is taller or smaller than the previous. As long as it is smaller than the initial, we should be able to go over it. 

3.) A ball pendulum  has a potential energy of 40J and is 20cm taller than its lowest point. What will the KE be at the bottom of the swing? How do you know? What will the PE be at position 3? How do you know? How high from the lowest position will the ball be at position 3? How do you know?

Here is the pendulum... 

The KE at the bottom will be 40J because PE= KE at it's lowest point. The Pe at the third position will be 40J because it is at the same height at when it began and PE depends on height. The ball will be 20cm from the lowest point from position 3 because you get so much energy out as you put in, therefore the height you begin at is the height you will end at. 

4.) With what force does a rock that weighs 10N strike the ground if dropped from a rest position of 10m high? The question cannot be answered unless you know more. Why? 

What we do know is that the work the rock does on the ground is equal to its PE before being dropped. What we don't know is the distance the ground that the rock penetrates into the ground. If we do not know the distance we cannot calculate the force. If we knew the time then using the impulse - momentum relationship relationship then we could, but we don't. 

5.) Listed below is the mass and speed of three different vehicles, A, B, and C. Rank them from greatest to least. 

a. Momentum (p= mv) 

b. Kinetic Energy 

c. Work done to bring them up to their respective speeds from rest 

Here is the algebraic work.... (answers posted below this picture)

Answers... 

A.) BAC 

B.) CBA 

C.) CBA 

Part four: Machines 

1.) What does a machine do? Does it decrease the amount of work put in or the amount of force used?

A machine decreases the amount of force by increasing the distance.

2.)  Label where the work in and the work out is occurring on the ramp.

Answer...

3.) What is the relationship between the work in and the work out?

The relationship is work in equals work out. 

4.) What is the efficiency formula?

5.) What is the ratio of work out to work in when a machine reaches maximum efficiency?

It is a 1:1 ratio. 

6.) When maximum efficiency is reached, there is an absence what three things?

There is an absence of heat, light, or sound. 

Examples and Practice Problems 

1.) Your cat suddenly became a youtube sensation like grumpy cat. Your cat decided he would like to move across town to live in the high end kitty condos. You are pushing his 200N box up the ramp. The ramp is 10m long and goes to a height of 5 meters. How would you know the potential energy of your box and your cat's box compare? How do you know? When did you do more work, going up the ramp or lifting the box into the truck? How do you know? What is the amount of work done?

The potential energy would be the same because the change in kinetic energy is the same. I know this because work and the change in kinetic energy is the same. I know that work is the same because machines don't decrease the amount of energy needed, they reduce the amount of force applied by increasing the distance. 

Diagram for the amount of work done... 

Answer....

2.) On the pulley system below label where the work in and out are. 

Answer...

3.) Scissors for cutting paper have long blades and short handles, whereas metal-cutting shears have long handles and short blades. Bolt cutters have very long handles and very short blades. Why is this so?

Scissors and shears are levers. The applied force is usually exerted over a short distance for scissors so that the output force is exerted over a relatively long distance. With metal cutting shears, the handles are long so that a relatively small input force is erected over a long distance to produce a large output force over a short distance. 

4.) If a Ferrari were to have a 100% efficient engine, transferring all of the fuel's energy to work, would the engine be warm to the touch? Would its exhaust heat the surrounding air? Would it make any noise? Would it vibrate? Would any of its fuel go unused? 

The engine wouldn't be warm to the touch. The exhaust heat wouldn't heat the surrounding air. The car wouldn't make any noise. The car wouldn't vibrate. None of the fuel would go unused. All of this is because when a machine is 100% efficient, none of the energy is lost to light, heat, or sound. 

5.) Why is a 1:1 pulley system not a simple machine? 

It doesn't reduce anything, the force and distance are the same. 

Unit 4: Blog Summary

Welcome back, my physics friends! I know it's been a while, but do not fear! I'm back in session now and have a great unit for you. In this new unit we learned about four more key and exciting concepts in physics....

1.) Rotational and Tangential Velocity

2.) Rotational Inertia and Conservation of Angular Momentum

3,) Torque and  Center of Mass/ Gravity

4.) Centripetal and Centrifugal Force

Just like in the last semester's units, I learned of numerous formulas, concepts and everyday applications. What sets this unit apart is that it was generally exciting to find things out such as why a train doesn't run off the tracks or why an ice skater goes faster when they pull their arms in. All of this and more will be answered below.

Part one: Rotational and Tangential Velocity

1.) What is tangential speed?

It is the direction of motion tangent to the circumference, the linear speed of something moving along a circular path.

2.) What are the units it's measure in?

It is measured in m/s or km/h. 

3.) Does tangential speed depend on the radial distance (distance from the axis)?

Yes, yes it does.

4.) What tangential speed directly related to?

It is directly related to rotational speed.

5.)  What does rotational speed involve?

It involves the number of rotations or revolutions per unit of time.

6.) What do all parts share?

They share the same rate of rotation/ number of rotations/revolutions.

7.) What unit is rotational velocity measure in?

It is measured in RPM's ( revolutions per minute).

8.) Is there speed in the center of the rotating platform?

No, there is not speed, just rotational.

9.) Keep this in mind...

Examples and Practice Problems (Some exercises from our textbook) 

1.) How are train wheel designed so they stay on the track?

Train wheels are tapered with the fat/wider part on the middle, the more narrow part on the outside. All parts of the wheel gave the same rotational speed, but the wider part has a greater tangential speed. This difference causes the wheels to curve when the wider part is on the track. The wheels curve inward, setting the train in the middle when it is in the middle of the track.

2.)  Look at the adorable kids on the merry-go-round. Specifically look at the girl sitting down (kid a) and the boy sitting behind her to her right (kid b). Which kid has the greater....

a.) Tangential velocity and why?

Kid B has the greater tangential because he is farther from the axis of rotation. 

b.) Rotational velocity and why? 

They have the same rotational velocity because their distance to the axis of rotation doesn't matter. They will have the same number of rotations around the merry go round. 

2.) An automobile speedometer is configured to read speed proportional to the rotational speed of its wheels. If larger wheels, such as those of snow tires,are used, will the speedometer reading be high, low- or no different?

Lower because the bigger wheel will cover more distance per revolution and the speedometer is only accounting for the revolutions for the smaller tire. 

3.) Fill in the blanks for the following....

a.) Gears work by having the same ________ velocity, but different ________ velocity. 

b.)  Train wheels autocorrect by having the same ________ velocity, but different ________ velocity. 

Answer for a: tangential/ rotational 

Answer for b: rotational/tangential 

Part two- Rotational Inertia and Conservation of Angular Momentum 

1.) What is rotational inertia?

The property of an object to resist changes to spin, A.K.A how much an object is willing to spin. 

2.)  What causes it to increase or decrease (i.e what does it depend on)?

The location of the mass in relation to the axis of rotation. 

3.) What does the conservation of rotational/angular momentum mean? 

It means once you start to spin you will continue to spin. 

4.) What two things affect the amount of rotational/angular momentum? 

The two things that affect it are rotational velocity and rotational inertia. 

5.) If something has a high amount of rotational inertia, will it be more or less likely to spin? 

It will be less likely to spin. 

Examples and Practice Problems (Some exercises taken from our  textbook) 

1.) Why was the meter stick with the masses closer to center easier to rotate?

It has a small amount of rotational inertia so it is easier to rotate. 

2.) Why do runners bend their legs when they run rather than keeping them outstretched?

They bend their legs because it brings their mass closer to their axis of rotation, decreasing their rotational inertia.

3.) An ice skater is spinning with his arms close to his body. Is his rotational inertia high or low? Is his rotational velocity high or low?

His rotational inertia is low. His rotational velocity is high. 

4.) The same ice skater now stretches his arms outward. What happens to his rotational inertia? What can you predict will happen to his rotational velocity? 

His rotational inertia is high. His rotational velocity is low. 

5.) Which would win a race down a ramp - a solid steel ball or a hoop and why?

The solid steel would win the race, believe it or not. The ball would win because its mass it closer to the center versus the hoop whose mass is more concentrated toward the outside. 

6.) Which would win a race down a ramp - a frozen bottle of water or an unfrozen bottle of water and       why? 

The frozen water bottle would win because it, like the steel ball, has it's mass concentrated in the center. On the other hand, the unfrozen water bottle's mass isn't solid and is moving around the outside of the water battle rather than remaining in the center. 

7.) Why are lightweight tires preferred over lightweight frames in bicycle racing?

Hopefully you know the answer by now! However, just in case, I will write it out. The light weight tires mean you have a low rotational inertia so it will spoon easier. When you have a heavy frame the mass will be away from the axis of rotation, so it will remain in the middle A.K.A less likely to rotate. 

8.) A large amount of soil is washed down from the Mississippi river to the Gulf of Mexico each year. What effect does this have on the length of the day? 

The day would get longer. 

Part three- Torque and Center of Mass/ Gravity 

1.) What does a torque cause?

It causes rotation. 

2.) What two things does torque require (i.e What is torque equal to)?

It requires a force and lever arm. 

3.) What is the formula to find the torque of an object?

Torque= Force x Lever Arm 

4.) What is a lever arm? 

It is the distance from the axis of rotation to where the force is applied. 

5.) When something is balanced, what do I know about the clockwise and counter clockwise torques?

 They are equal. 

6.) What are three different ways you could get a large torque?

 You can increase your lever arm, force, or both. 

7.) How can you have a large torque without having a large force (i.e How can a very small force cause a large torque)? 

If you have a large lever arm then you only need to apply a small force to get a large torque. 

8.) What is the center of mass? 

The average position of an objects mass. 

9.) What is the center of gravity?

The specific point on all objects that gravity acts on. 

10.) What two things cause you to be more stable?

The two things that cause you to be more stable are lowering your center of gravity and widening your base of support. 

11.) What will an object need to do in order to fall over? 

An object will need to rotate outside of its base of support. 

Examples and Practice Problems (Some exercises taken from our textbook) 

1.) Why do more objects tip over when the center of gravity us not over their base of support?

This is because it creates a lever arm, which combined with force creates a torque. Torque causes rotation. 

2.) Why is putting a door stop closer to the handle better than putting it close to the hinge? 

By putting the door stop closer to the handle, the lever arm is lengthened which requires less force than if the lever arm was smaller. 

3.)  Why do wrestlers bend their knees and have their feet shoulder width apart when wrestling?

They do this to lower their center of gravity and increase their base of support. The wider base of support and lower center of gravity makes it harder to rotate outside of the base of support, in turn making them more stable. 

4.) Where would you place your finger if you were trying to balance a hammer and/or a broom?

For a hammer or broom you place it near the head of the tool. You place it near the head of the top because that is where the center of gravity is. The lever arm then doesn't need to be nearly as long to equalize the counterclockwise and clockwise torques. 

5.) The rock and the meter stick balance at the 25cm mark, in the picture below. The meter stick has a mass of 1kg. What must be the mass of the rock?

Answer....

6.) Is the net torque changed when a partner on a seesaw stands of hangs from her end instead of sitting? (Does the weight of the lever arm change?)

No, it does not change. 

7.) Can a force produce a torque when there is no lever arm? 

No, it cannot because the formula for Torque = Force x Lever Arm. 

8.) Why is a long pole more beneficial to a tightrope walker if the pole droops? 

It is more beneficial because it widens his base of support, making it harder for him to rotate out of it. 

9.) The center of gravity of the three trucks parked on a hill are shown by the X's. Which truck(s) will tip over? 

It will be the first one because when you draw a line from the red x then went diagonally, only the last two truck's lines would be over the base of support. 

10.) A long tack balanced like a seesaw supports a golf ball and a more massive billiard ball with a compressed spring between the two. When the spring is released, the balls move away from each other. Does the track tip clockwise, tip counterclockwise, or remain in the balance as the balls roll outward? 

It will remain balanced because the counterclockwise and clockwise torques are equal. The torques are equal because the billiard ball will have a big force, but a short lever arm, The golf ball will have a small force with a large lever arm. 

11.) Why are football players less likely to be pushed over when they keep their legs shoulder width wide vs. feet together?

They are less likely to be pushed over because they have a wider base of support. When they have a wider base of support it is harder to rotate outside of it.

12.) A long stick is balanced as is shown below. What is the weight of the stick? (show work)

Part four- Centripetal and Centrifugal force 

1.) What is a centripetal force?

It is a center seeking force.

2.) What is a centrifugal force?

It is a lie! This is because it is a fictitious force.


Here is an example of centripetal force to give you an idea of what that might look like..

3.) The velocity of an object is always ________ to the circle?

Answer: Tangent

4.) What force causes you to fling out when turning in a car?

It is the centripetal force.

Examples and Practice Problems (Some exercises from our textbook) 

1.) What force causes the water to fling out in a salad spinner whilst spinning it? (See the video below  if you are unaware of what a salad spinner is, looks like, or how it functions.) (Answer is posted below video.)



It is the absence of centripetal force on the water. This is because if there were centripetal force then the water would curve when it flew out instead of going straight. Centripetal force is the key component in something wanting to curve. 

2.) Describe the force that keeps you in the car when turning: what is it, what direction does it act, and how does this work?

The force is centripetal force. It acts in the inward direction because it is a center seeking force. 

3.) What direction does an object move in a circle compared to the force exerted on it that keeps it in the circle? (see picture in question number 8)

It moves tangent to the circle. 

4.) Why are race track curves built at an angle?

They are built at an angle because the F weight and F support add up to create a centripetal force which keeps the driver and the car on the track.

5.) Can an object move along a curved path if no force acts on it? Explain

6.) You are on a race track and it's been snowing! The ground is covered in a thin layer of frost and friction is need for you to round the curve of the final lap! If the track is banked, friction may not be needed at all. What, then, supplies the needed centripetal force?

The F support and F weight supplies the needed centripetal force. 

7.) Are satellites stationary above the earth? How do they stay close to the earth without flying into space and also not hitting the earth?

No, they're not stationary. They stay close to the earth because they're given a certain velocity, not too fast or too slow, so that the centripetal force of gravity pulls it in close to the earth.

8.) Label the centripetal force and the tangential velocity below and it's direction....

Answer.... 

9.) The car below is on a banked racetrack. There is a centripetal force acting on this car keeping it on the track. With labeled vectors, show where this centripetal force comes from.  

Answer... 

With a flying object it is similar, but with one small difference. See if you can spot the difference..... 

Answer: The difference is that there is no F support. Instead of F support, there is F tension.

You made it to the end! I know that was a lot of work, but you are made better for it!