Unit 4 - Energy

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If I have a book sliding along a frictionless surface at a constant velocity and then push it up a ramp that later flattens out, and the book slides with a slightly lower velocity than it had initially, the book-earth energy graph would look like the illustrated graph. The energy in the system can be modeled by Ei + Wext = Ef. The external work is positive, meaning that the force I applied to the book increased the system’s energy. This energy is seen through an increase in gravitational potential energy (GPE). After accounting for the 1 unit decrease in kinetic energy, we can conclude the following about my application of force to the block as it moves up the ramp: the applied force from my hand has a smaller parallel component than gravity. I can conclude this because the kinetic energy (KE) decreased, indicating that the speed of the book decreased, showing that acceleration opposite the book’s velocity occurred. As the book goes up the ramp, it looks like this (see attached diagram and FBD):

Because the block is slowing down, we can conclude that mgsin() has a greater magnitude that Fa, and they act in opposite directions. As the block goes up the ramp, it gains potential energy relative to the surface of the earth because of its increased height, and its final motion on the flat portion has a greater GPE than initial and a slightly lower KE. The difference between Ef and Ei is 4 units of energy (I assume the graph is using joules), which is equal to the work done by my hand times the distance through which I apply the force to the block.

Hi Peter! Happy to be joining Fiveable! In response to this prompt, I created a PASA and timed myself for 15 minutes to see what I could come up with. I would really appreciate your feedback on it so that I can practice knowing my strengths and weaknesses. Have a great day!

Hi Daniel! Welcome to Fiveable!

Here’s a couple of tips about your answer:

  1. Nice job interpreting that we need to have KE decrease, PEg increase and some outside force do work on the system.

  2. Make sure at the beginning of your paragraph you clearly define the system. Are we talking about just the sphere (just KE allowed), sphere-Earth (KE and PEg allowed), or sphere-spring-Earth (KE, PEs, PEg allowed)?

  3. PEg increasing means we need to have a change in height, but I didn’t see anything in your explanation that mentioned a hill or ramp or launching the sphere upwards.

  4. Friction could reduce the KE of the object, but the overall work is positive, not negative, so there must be another force that will result in the net force being positive.

Hey Peter! Based on your feedback, I came up with this FRQ. I worry that I am overcomplicating this. I am now realizing that I probably could have created a scenario without a spring, as the PE of the spring is always 0 anyways.

Hi Daniel,
This is better, but you’re still over complicating the scenario. Because PEs was 0 at the beginning and end, you don’t need a spring at all. It’s ok that you included it but then you need to jump through so many hoops to make it work.

I’d do something much simpler. We need to be moving at the beginning (KE), gain some energy (positive work), and end up with a bit less KE but more PEg at the end.

Anytime we’re looking at increasing PEg we need to change height. That means a ramp or hill or going upwards into the air.

Possible Scenarios -

  1. A car driving down the road when it comes to a hill. The driver pushes the gas pedal to increase the car’s mechanical energy, but it’s not enough to keep the car’s speed constant as it goes up the hill.
  2. A student is pushing a refrigerator into a moving truck. The fridge needs to go up a ramp to get into the truck, so the student pushes harder on it (does work). However the student can’t push hard enough to keep it moving at a constant speed.
  3. A vertical lifting situation where 0 PEg is defined as the starting position of the moving object.

Hope this helps.

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