Laboratory Activity 10: Work and Energy

Laboratory Activity 10: Work and energy

Objectives

• Practice calculating work.
• Develop the idea of kinetic energy.
• Discover the relationship between work and energy.

Equipment

• Dynamics track.
• Motion detector.
• Force sensor
• USB link.

• Computer with DataStudio
• Dynamics cart
• Cart mass
• Books or box to prop with

Activity One: Work on a cart

In a previous class you helped come up with the physics definition of Work, which is force applied over a distance. Mathematically, it is expressed

W = F * d * cos

where  is the angle between the direction of force and the direction of motion.

Experiment 1: Lay the track on the table with a couple of books or a plastic box under one end so that the track is on a slope of 5o to 10o relative to the table. Place the cart on the track at the bottom and the cart mass in it. Connect the force sensor to the computer and hook it on the cart. Pull the cart and mass up the track at a slow, steady rate, while recording the force you are exerting on it.

Question 1a: How much force does it take to move the cart up the ramp at a steady rate?

Question 1b: Are you performing work on the cart? If so, how much work must you do on the cart to get it from the bottom of the ramp to a place about 40 cm from the end? You can use the ruler markings on the track to calculate distance.

Question 1c: Are there any other forces that are doing work on the cart? Identify all the other forces acting on the cart and check if any of them have at least a component along the direction of motion. How much work is done on the cart by the other force(s)? (Don’t forget about direction.)

Question 1d: What is the total (net) work done on the cart by the force detector and the other force(s)? What is the net force on the cart as you move it up the ramp at a steady speed? Is the total work done on the cart consistent with what you know the net to be?

Experiment 2: Connect the motion detector to the computer and place it at the top of the ramp, making sure it is on cart setting. Save the file WorkEnergy.ds from the web page and open it in DataStudio. When the file is opened, you will see a small calculation window that has a place for you to enter the size of the component of the gravitational force along the ramp. Enter the value you got above for the force of gravity on the cart along the ramp and click the button “accept”. You will let gravity do positive work on the cart by letting it slide down the ramp, and check how that agrees with you calculations above. Place the cart where you stopped in the first part, start taking data and let it roll down to the bottom.

Question 2: What is the value of the work done when it hits the end of the track? How does this number compare to your calculations above? If they are not reasonably close, go back and check your calculations and experiment.

Activity Two: Work, velocity and kinetic energy

In the second case you investigated, there was net work done on the cart since there was no other force opposing gravity down the ramp. You will also notice that while the first case the cart moved at a constant speed, in this case it speeds up. Let’s investigate the relationship between work and velocity. Partially hidden behind the Work vs. Time graph you have just been looking at is another graph called “Vel & vel^2”. Click on it at the bottom or in the navigation panel in the lower left-hand corner. The top plot shows velocity as a function of work done. The bottom shows velocity squared as a function of work done. Copy that graph and paste it below.

Paste graph here.

Question 3: Which quantity, velocity or velocity squared, shows more of a direct relationship with work? Do you think that the mass of an object would affect the velocity it gets? Imagine you were to apply the same force for the same distance to two carts, one of which was much heavier than the other. Which would have a larger final velocity?

In physics we define a quantity called “kinetic energy” to relate mass and velocity to the work done. It is defined as

KE = ½ m*v2

If you click on the calculator symbol labeled “KE” in the data window in the upper left-hand side of DataStudio, the calculation window will come to the front with a calculation for KE. Enter the mass of your cart (with the cart mass) in the box to set the value of m and click the button “accept”. Then display the hidden third graph, labeled “KE vs. Work” by either clicking on its icon in the lower-left Displays window or by minimizing the other graphs. Paste the graph below.

Paste graph here
.

Question 4: What is the relationship between kinetic energy and work (before the cart hits the end of the track? Are they proportional, the way that force and acceleration are proportional for a constant mass, or are they actually equal to each other?

Review question: (Skip if you are running out of time.) Theoretically, what should you have found for the force in Question 1a? Remember to draw the force diagram for the cart and calculate the force of the detector on the cart to move it at a constant speed. Note that each cart and each cart mass have a mass of 250 grams. Measure the length of the track and the height the one end is above the table to figure out your angle.

Summary

The following questions will help you get the main ideas out of this lab. You should find these straightforward questions, but take the time to talk it over with your team and write complete answers to these questions. You may find your answers here to be the most useful part of this lab down the road.

Summary 1: In the first case, when the net force on the cart was zero, what was the net (total) amount of work done on the cart by all the different forces? How was the cart moving after this work was done on it?

Summary 2: In the second case, when there was a net force on the cart, what was the net work done? How was the cart moving at the end? What happened to the work done on the cart? Where did that work “go”? What is the relationship between velocity, kinetic energy, and work?

Summary 3: In this lab you developed and understanding of how work relates to kinetic energy. State that relationship, and give an argument you could use to convince a friend or roommate who has not taken physics.