Otterbein University Department of Physics Physics Laboratory 1500-7

Name: ________________________ Partner’s Name: ________________________

EXPERIMENT 1500-7

WORK & ENERGY

INTRODUCTION

In this lab we will be rolling a cart down an incline. In class, we have already analyzed this system in terms of force and acceleration, but today we wish to look at the system in terms of work and energy.

The central result is the work-kinetic energy theorem:

Wtot = K2 – K1

Here Wtot is the total work done on the object, or equivalently, the work done by the net (total) force, as it moves from point 1 to point 2, and K is the kinetic energy:

K = ½ Mv2

ANALYSIS

We will study the cart both as it moves up and down the plane. As always, we begin with free body diagrams. In the space below, draw separate FBDs for the cart moving up the plane and down the plane. Be clear about which is which. Do not neglect friction. Take the x-direction to be up the plane and the y-direction perpendicular to the plane.

Next, apply Newton’s second law in each case to obtain the total force in the direction along the plane. Note that we will be measuring the friction force, so there is no need to express it in terms of the normal force. Just call its magnitude f.

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Otterbein University Department of Physics Physics Laboratory 1500-7

Let us choose x = 0 to be the bottom of the slope. Using the result for the net force, write an expression for the total work done on the cart as it rolls uphill, after it has moved a distance x up the slope:

Is this work positive or negative? Does the sign match what you expect from the work-kinetic energy theorem? Explain.

When the cart slides downhill, assume it starts at some initial point x = L. Again write an expression for the total work done when it is at position x. (As a check, note that when x = L this work should be zero.)

Again, check the sign of the work and verify that it agrees with the work-kinetic energy theorem.

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Otterbein University Department of Physics Physics Laboratory 1500-7

Finally, apply the work-kinetic energy theorem to the uphill motion, to find the kinetic energy at any point in terms of the initial kinetic energy (remember, the cart is moving to start with) and the distance up the track.

Repeat for the downhill motion. This time you can set the initial kinetic energy to zero, since the cart starts downhill from rest.

Now look at your results. You should see that if we plot the kinetic energy K as a function of position on the track x, we predict a line with slope equal to

– f ± Mg sin

depending on whether the cart is going uphill or downhill (which is which?). If this is not what you obtained, check with the instructor to resolve any issues.

Your task now is to measure these slopes and use the results to determine f and .

MEASUREMENTS

Set up the track as shown in the diagram. Put a book under the one set of track supports to lift it up distance d above the table.

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Otterbein University Department of Physics Physics Laboratory 1500-7

Measure the height of the track in two places (d1 and d2 in the diagram above) and the distance between those two places (not shown) to find θ, the incline angle of the track. Show your calculation of θ below (include a diagram to help).

Next, weigh your cart on a scale and record its mass.

M = _______________

Start the Logger Pro software. Configure it to use the motion encode cart as the sensor. (Experiment / Set up Sensors / Lab Pro 1 / click on the upper right box). Start a run and check which way x is increasing: make sure it’s large and positive at the top of the ramp, and small at the bottom. If it’s not, go back to the sensors box, click the drop-down on the picture of the cart, and select “Reverse Direction”. You can also select “Zero” if you like to set the current position of the cart to be x = 0. (Remember that picking up the cart and moving it will change this calibration.)

Logger Pro should show you two graphs and a mini spreadsheet showing the time, position, and velocity of the cart. Set up the cart at the top of the ramp. Start collecting data and let go of the cart. Select four different times during the run and copy the values for time, position, and velocity in the first three columns in the table below. Repeat for uphill motion, starting the cart with a gentle push.

Downhill:Uphill:

t (s) x (m) v (m/s) K (J)

Use the formula given earlier to determine the kinetic energy at each point in the motion. Show representative calculations below.

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t (s) x (m) v (m/s) K (J)

Otterbein University Department of Physics Physics Laboratory 1500-7

ANALYSIS

Use the mouse to copy the data from the “good” region of your graph (where the acceleration is constant) into an Excel spreadsheet, as shown in the figure below. Use the control-C and control-V shortcuts to copy and paste the data. Make sure to label your columns in the spreadsheet.

Let the computer repeat the exercise you did above, but using more values. Create columns for x and K. If you need help to create equations to fill out these values, ask your instructor. There’s an Excel cheat sheet on the last page of this packet. Make sure everyone in the group sees how this is done.

Have Excel create a plot of K vs x for each case – uphill and downhill. K should be on the vertical axis, x on the horizontal. (To make a plot, select the columns and use “Insert” / “Scatter Plot”.) If all is well, these data should appear to lie on a line. If not, go back and fix your results.

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Otterbein University Department of Physics Physics Laboratory 1500-7

Make sure every lab partner prints and staples a copy of both plots to the back of this worksheet. Remember that you will be graded on the same criteria (labeled axes, units, etc.) as you would for a hand-drawn graph.

Now have Excel determine the slope of the best-fit line in each case. What are the units of these numbers?

mup = _________________ (uphill)

mdn = _________________ (downhill)

Using your earlier analysis, determine from these values the magnitude of the frictional force and the component of the weight along the track. Be sure to specify units.

f = _________________

mgsin= _________________

Use the latter result to determine the angle your track makes with the horizontal. Compare to your earlier determination.

Next, return to LoggerPro and add an acceleration window. Collecting data, roll the cart up the hill and let it come back down. Look at the acceleration plot. What happens at the top of the hill? Explain, using your earlier analysis.

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Otterbein University Department of Physics Physics Laboratory 1500-7

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Otterbein University Department of Physics Physics Laboratory 1500-7

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