Conservation of Energy in 2D Lab: Elastic or Inelastic?

Credit: http://dev.physicslab.org/DocumentPrint.aspx?doctype=2&filename=Momentum_MomentumCollisionsAngle.xml

Background: In this lab we will investigate a collision two-dimensions by allowing a cart to roll down an incline and collide obliquely with a stationary, cart bearing. Afterwards we willcalculate the total kinetic energy of both cartsbefore and after the collision to determine what percentage of the energy was lost during the collision.

Purpose: 1) To determine if a collision between two objects is elastic, inelastic, or perfectly inelastic.

Hypothesis: Please write a hypothesis for each of the purposes prior to starting the lab. Remember that your hypothesis is just what you believe before the experiment; it does not have to be correct! You need a hypothesis to compare your results to in the conclusion.

Materials: ramp white paper carbon paper 2 carts

Ruler protractor scale

Procedure 1:

1) Create a ramp using wood and Bristol board. It needs to have a flattened end (it should have a slope with a gradual ending so the cart does not “jump” when it hits the table and so the cart is only travelling in a horizontal direction).

2) Place the carbon paper “inky side up” under the white “target” paper.

3) Place the flat portion of the ramp on top of the white paper and use a pen to mark its edges.

4) Place one cart slightly off to the side of the ramp so that the other cart will strike it off-center after rolling down the ramp.

Allow the other cart to roll down the ramp. After the cartscollide, they will leave tracks on the BACK of your white target paper. Notice that you will be viewing a mirror image, that is, the cart that was on the paper will be the track on the bottom and the cart that was going down the ramp will be the track on the top. Label which line represents which cart.

6) "Connect the dots" for each track. Extend the lines back until they cross.

7) Once the intersection has been found, use a protractor to draw in the "x-axis" for the collision. This isa line which is perpendicular to thefront edge of the ramp (which was drawn in step 3) which passes through the intersection of the tracks.

8) Use a protractor to measure the angle that each track makes to the "x-axis." Remember to read the protractor carefully, thinking about significant figures. Record the measurement directly on the white paper and include this as raw data in the lab report.

How many decimals should be recorded? Why?

Observations:

1.  How high was the top of the ramp above the top of the table/paper in cm? ______

2.  What was the mass of the carts in grams? m1 = ______m2 = ______

3. At what angle did the cart going down the leave the collision? θramp = ______

4. At what angle did the cart on the paper leave the collision? θpaper = ______

Analysis Questions:

Procedure 1:

1)  What is the velocity of the stationary cart prior to the collision?

2)  Using conservation of energy methods, determine the velocity of the rolling cart when it reached the bottom of the ramp, prior to its collision with the stationary cart. (We have not covered kinetic energy due to rotation but you should remember from grade 11 that total energy is conserved in a collision. In this lab, the energy of the rolling cart starts off as potential energy due to height and at the bottom of the ramp the energy is kinetic energy along with kinetic energy due to rotation. So here is the formula you need!) This formula states that the potential energy before the cart rolls down the ramp is equal to the kinetic energy and the rotational kinetic energy at the bottom of the ramp (ie, just before the collision).

Velocity of the rolling cart at the bottom of the ramp (in m/s)= ______

2) Determine the velocity of each cart (in m/s) after the impact.

HINT: In this lab, each of the carts leaves the collision at a unique angle and speed. To determine just how fast each cart is moving, look at the equations for conservation of momentum in both the x- and y-directions. Remember that the cart rolling down the ramp entered the collision moving completely in the x-direction (ignore the vertical motion as the ramp has a flat bottom).

By looking at the x-direction, an equation with two unknowns will arise.

By looking at the y-direction, an equation with two unknowns will arise.

Solve these simultaneous equations using substitution, elimination, or matrices.

3) Calculate the total kinetic energy of the rolling cart before the collision in Joules.

HINT: Remember that the total KE before the collision is actually the rolling cart's potential energy at the top of the ramp.

4) Calculate the total kinetic energy of the rolling cart after the collision in Joules.

HINT: Remember that both carts rotate as well as translate. This means you need to use the formula (not just ½ mv2) for the cart’s energy after the collision.

5) Calculate the total kinetic energy of the stationary cart before the collision in Joules.

6) Calculate the total kinetic energy of the stationary cart after the collision in Joules.

7) How many Joules of kinetic energy was lost during the collision?

8) What percent of the rolling cart’s original kinetic energy does this loss represent?

9) Is this an elastic, inelastic, or perfectly inelastic collision? How do you know? Is this what you expected?

Conclusion: Explain the purpose of the lab and if those purposes were met and how. Explain your results. Confirm whether or not your hypothesis was supported by the results. Account for uncertainties and errors. State the errors and what type of errors they are. Discuss any new questions or discoveries that emerged from the experiment. If you tried the experiment more than once, describe the reasons for doing so. Discuss changes that you made in your procedures.

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