University of Virginia
Physics Department

## Change in Energy of a Cart on a Ramp (Version B)

A Physical Science Activity

NOTE: There are two versions of this activity. Both use probes and graphing calculators. Version A uses the CBL and a motion detector. Version B uses the new CBR (Calculator Based Ranger) which is a TI-made motion detector that does not need the CBL. It has internal programs and is connected directly to the TI-83 or 83 plus calculator.

2003 Virginia SOLs

• PS.1
• PS.6

Objectives

Students will

• understand the quantitative relationships between total, potential, and kinetic energies;
• measure and compare values of kinetic and potential energies;
• use the CBR calculator system to calculate instantaneous velocities;
• use the following skills: observing, comparing, inferring, predicting, and experimenting with variables, and plotting graphs of variables.

Motivation for Learning

Demonstration: Energy of a Falling Ball

Materials

Several different balls, preferably of the same size, but of different mass (for example, a racquetball and a billiard ball).

Background and Procedure

We want the students to obtain a qualitative idea of the transfer of energy from potential to kinetic. The harder the ball pushes on the hand that catches it, the more kinetic energy it has at that point. If you drop a ball from one hand to the other (one higher than the other), there are certain factors that give the ball a different amount of kinetic energy at the end.

• If you change the height from which you drop a ball to a higher height, then the ball will have more velocity and more kinetic energy at the end. You can show this by having one hand as low as possible, and dropping a ball from the height of your head, and then from as far up as you can reach, and note the extra effort you exerted to stop the ball the second time. This shows that the ball has more kinetic energy when it falls a greater distance.
• If you take a heavier ball and drop it from the same height as the other lighter ball, there is also more kinetic energy and it requires more energy to stop it. This shows that a heavier object at the same height as a lighter one will have a greater potential energy.

Write down the equation for potential energy and show that the mass and height are dependent variables (U = mgh, where U is potential energy, m is mass, g is the acceleration of gravity, and h is the height of the object. Remember that the zero of potential energy is arbitrary, so h can be measured from anywhere you choose). Let the initial height be h1 and the final height be h2.

Write down the equation for kinetic energy (KE = ½ mv2) and show that it is dependent on mass and speed of the object. You can show that kinetic energy is higher with a greater speed by throwing the ball into your other hand and expressing the extra effort you exert to stop the ball. Similarly, show that for a constant speed, a more massive ball seems to have more kinetic energy and requires more force or effort to catch.

Energy can neither be created nor destroyed, so the amount of energy lost as potential energy when it was high up in the air should equal the kinetic energy gained at the end of travel. This is what we will test in the experiment, whether the term m*g*(h1-h2) (where (h1-h2) is the actual distance fallen) is equal to ½ *m*v2 (ending kinetic energy).

In order to do this, we must measure the difference between starting and finishing height Dh, the velocity at the end, and the mass of the object. In order to calculate the velocity at the end we will use the CBR. Since we want to slow down the whole process of the falling, we will use a ramp and cart rather than a falling ball. We will use the CBR that connects to the TI-83 graphing calculator to follow the velocity patterns of the cart as it descends the ramp.

1. At the top of the hill you have lots of gravitational potential energy, which is the energy stored in the gravitational force attracting you toward the Earth.

2. As you loose altitude and pick up speed, more of your gravitational potential energy is converted into kinetic energy. The amount of kinetic energy you gain is exactly equal to the amount of potential energy you loose so that your total energy remains constant.

3. The heavier cart will feel a larger gravitational force downward because it has more mass, so it would seem like it would move faster. But, because it has more mass than the other one, it will want to stay at rest more (that is, its inertia is higher), so it takes more energy to move it. For these reasons the heavier cart will go at the same speed as the lighter one.

### Student Activity

Materials

• Texas Instruments CBR Ranger motion detector.
• TI-83 (or TI-83 plus) graphing calculator with cable link. Also works with TI-82, but note that programs appropriate to the TI-82 will need to be obtained.
• The following programs (Note: these programs can be downloaded for any of the TI calculators at http://www.ti.com/calc/docs/cbr.htm and clicking on your particular calculator in the CBR Program Archive.
• Program Ranger is in CBR.
• Wooden board (about 2 m long and at least 20 cm wide)
• Books or something large to prop board on
• Cart (could be a toy truck or physics cart, anything that rolls with little friction).
• Large sponge or something soft to stop cart
• Mass scale (digital balance or triple beam balance)

Procedure

1. Measure the mass of the cart on the mass scale.
2. Connect the CBR unit to the TI Calculator with the unit-to-unit link cable using the I/O Ports located on the bottom edge of the units. Turn on units.
3. Stack a few books (or something similar) beneath a wooden board, as shown in the setup diagram. Place the motion detector at the top of the ramp and position the dynamics cart at least 50 centimeters from the motion detector (you will receive spurious results if the motion detector is closer than 50 cm to the moving object). Place the sponge or something soft at the bottom of the ramp to catch the cart.

4. Measure the height of release of the cart (you can experiment with average value of height) and the height that the cart hits the sponge. It is important that you subtract the height of the cart at the end of the trip from the original height so that the change in height Dh is known to determine the potential energy.
5. Run the RANGER calculator program. Program the calculator to perform a velocity vs. time measurement and for the initiation of data recording by pressing the trigger button on the CBR. Start the velocity vs. time measurement by pressing the trigger button and release the cart, making sure not to give the cart any initial velocity when letting go. (Note: The RANGER program asks for a time period that the experiment will run and calculates the reading interval it needs to utilize all of its storage capacity for that given time. Hence if a longer time is used then the intervals of measurement are long, a short time gives smaller intervals. We found that a 5 s time interval works well.)
6. When the cart hits the stop, stop the calculator's measurements.
7. Read off the velocity at the point it hit the stop (where the arrow is pointing. The rapid oscillating values after this time are due to the bouncing back and fourth of the cart after it hit and should be ignored).

8. Calculate kinetic energy ( ½ mv^2) and potential energy loss {m*g*(h1-h2)} and compare results. Perform this calculation for varying heights of the ramp.

Data Sheet

 Trial #1 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

 Trial #2 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

 Trial #3 Potential Energy Calculation Measurement: Mass of the cart-M (kg) Measurement: Original height (m) Measurement: Final height (m) Calculation: Difference in height- h1-h2 (m) Calculation: Difference in potential energy U = M*g*(h1-h2) acceleration due to gravity, g = 9.8 m/s2 Kinetic Energy Calculation Calculator Measurement: Final velocity-v (m/s) Calculation: Final kinetic energy KE = (1/2)*M*v2

1. Why aren't the potential and kinetic energy readings that we compare exactly the same?

2. Pretend you were sliding down a snow hill on a sled with no friction, just like the cart in the experiment. During your descent of the hill describe how your gravitational potential energy, kinetic energy, and total energy change.

3. What would happen if we used a heavier cart in the experiment? Would it have gone faster or slower, or the same speed? Why?

Assessment

Data sheet to be completed during the laboratory.

Students with special needs