Here is your first lab encounter with energy, in particular mechanical energy. You'll see how the motion of an object embodies the transformation between gravitational potential energy and kinetic energy. You'll also see how work can change the potential energy of an object.
Computer-based measurement system, cart, track, and force probe.
String and pulley
Assorted clamps and rods
1. Transformation of energy from Gravitational Potential Energy to Kinetic Energy
Start by waking up the Logger Pro software by clicking on the icon named "Week 1" on your computer desktop.
In this part of the lab, you'll investigate the motion of a dynamics cart down an inclined track. Tip the track up at an angle so that the sonic ranger is at the high end, using the post and clamp setup to hold it in place.
The thing to measure here is a simple downward rolling motion of the cart, after you release it from a particular height. Pick a convenient spot on the track from which to release the cart, and measure the height of the track at the midpoint of the cart. Now, practice gently releasing the cart and letting it roll until it reaches the end of the track. Make sure you can recognize in your data the moment when the cart hits the table upon reaching the end of the track. (One team member's job is to stop the cart from falling onto the floor.)
When you have obtained clean data, start a table with two columns, the
height change of the cart (height of release minus height at the end of the
motion) and the cart's velocity at the end of the track. Enter the first
two values in the table.
Now, try releasing the cart from three other heights along the sloping track. Record in the table the height and the velocity at the end of the track. When you have done this, make a third column in the table for v2. Fill in that column was well.
On a piece of graph paper, draw a graph of v2 versus
height. What kind of relationship do you see in the graph?
Now, adjust the slope of the track to a substantially different value.
Make another table, and use it to record a set of final velocities from motions
that start at several different heights, including some of the same heights
as in the previous set. Also calculate v2.
Make another graph. What relationship do you see? How does it compare to
the first graph?
Can you explain why you should have expected the same graph in each case?
2. Work and kinetic energy for moving cart
In this section, in addition to the Sonic Ranger you'll also use a "force probe" that lets you measure the force applied to a cart. You will then use the Logger Pro software to evaluate the sum of F*Dx.
First, close Logger Pro to get out of the setup you used in part 1 of the lab, then launch it again using the icon labelled "Week 2".
Attach the force probe to the top of the cart with the mounting bracket. Cut a piece of string long enough to stretch the length of your track. Tie one end to the force probe's hook at the front of your cart, and make a loop in the other end to which you can attach a mass. Start by hanging a 0.1 kg mass there.
Practice suspending the weight, making sure it is still, then releasing the cart and recording data. (One team member needs to take on the job of ensuring that the cart does not go flying onto the floor!) When your team has good technique, record some data. Note: Make sure that you zero out all sensors by clicking on "Experiment", clicking on "Zero" on the menu that comes up and then checking off "Zero all sensors", and clicking on OK.
(If your data does not look clean, here are a couple of hints: a) Make sure that the spring-loaded plunger on the end of the cart is pressed in and stays in. b) Keep the lab table all along the track scrupulously clean and empty. c) Keep everyone out of the way and still during data-taking.)
When you've got the apparatus set up, practice letting the mass go and recording clean data for force applied to the cart and for distance. Stop when you've got a good run.
Look at the data, and identify the region where a roughly constant force
was applied. What time interval was it in your case?
On the graph paper that you used for the first part of the lab, sketch both the distance graph and the force graph.
If the force does stay pretty constant over the range you've found, is
it also the case that the distance data look more or less like a parabola?
Switch the Graph Layout to "One Pane", and look at the graph of force vs.
time. Now, transform this graph into what you need for calculating work:
a graph of force vs. distance. You can make the change by clicking on the
word "time" under the x axis, and choosing "distance" instead in the dialog
box that comes up. Make a sketch of the graph of F versus x on the graph paper.
Does this graph look pretty similar to the graph of F versus t,
or does it look rather different? If so, how does it differ?
Now, it is time to calculate the work done on the cart, by summing up F*Dx. Here’s how: First, click on the "measurement
cursor button", and use the mouse to drag the cursor across the region of
the data where the force is being applied. (Be sure to include the whole
region where the force is being applied.) Then click on the "Integral" button
on the toolbar. (It is the one with a white sort-of-rectangular area underneath
a curve.) What is the value that you find? (Be sure to note the units.)
Does this value look reasonable? To answer this question, make a separate
estimate of the sum of F*Dx from your sketch
of the graph F versus d. What is the width, in meters of the
range of motion where F was roughly constant. What is approximate value
of the force over that region?
Calculate the product of the average force and the distance.
Does the value agree (to a reasonable precision) with the integral that
you calculated with Logger Pro?
If there is a real discrepancy, can you think of a possible reason (at
least an explanation that explains the sign of the discrepancy)?
3. Thinking back on what you have learned.Each student should be responsible for understanding the answers to all of these questions before leaving your studio.
How do the results you found in the first part of the lab show that there is a fixed "exchange rate" between how far an object falls and how much it speeds up?
Is the "exchange rate" the same for something that drops freely and something
that rolls (with negligible friction) down a track?
If you haven't already done so in your answers to the last two questions,
write down an equation that describes the total energy of of the cart, and
state whether it is conserved.
Concerning the measurements in the second part of the lab:
Considering just the cart, can you say that work changed its kinetic energy?
Changed its total energy?
Considering both the cart and the mass together as one system, did their
kinetic energy change? Did their total energy change? If you answer is different
in any way from your answer for just the cart, explain the difference.