Studio Physics I
Forces and Motion in Coupled Systems
Equipment:
A cart is pulled along a level track by a string that passes over a pulley and is attached to
a mass that hangs down. The set-up is exactly the same as the one we have used in
previous activities. You will be able to vary the mass of hanging mass, the mass of cart
(above a minimum mass), and the length of the string. The mass will fall through a
distance that is much less than the length of the track. That is, the mass hits the floor
significantly before the cart hits the end of the track. You will also have a motion
detector and LoggerPro software to use in making measurements.
Individual Preparation:
You should answer the following five questions individually on your activity write-up:
1.
2.
3.
4.
Make a sketch of the problem situation (equipment).
Decide on your origin and coordinate system and draw it.
Assign variable names.
What is the relation between velocity at the instant the falling weight hits the floor
and the velocity of the cart at the end of the track?
5. Write down what principles of Physics you will use to solve this problem and derive a
formula for velocity in terms of acceleration and distance the weight falls.
Team Work:
The first thing that you should do is to compare everyone’s work on the questions
above. In particular, you should compare your group’s expressions for the launch
(final) velocity of the cart in terms of the distance the hanging mass falls and the
acceleration of the cart. The expression should not contain the time variable. Do all
of you agree on the expression? If not, come to some consensus on what is correct.
6. Free Body Diagrams and Force Equations: Draw separate free-body diagrams for
the cart and hanging mass after they start accelerating. Check to see if any of these
forces are related by Newton’s 3rd law (Third law pairs). An example of a third law
pair is as follows: If you push the cart, there is a force from your hand on the cart.
There is also a force from the cart on your hand. These two forces are a Newton’s
third law pair. Newton’s third law pairs are forces between the same two objects,
but which object is exerting the force and which is being acted on are exchanged. If
there are any, list all Newton’s 3rd law pairs in this problem. For easy reference, it is
useful to draw the acceleration vector for the object next to its free-body diagram.
The origin (tail) of all vectors for one object should be at the same place. For each
object, write down Newton’s 2nd law along each of the axis of the coordinate system
(X and Y). It is important to make sure that all of your signs are correct. For
example, if the acceleration of the car is in the + direction, is the acceleration of the
hanging mass + or -? Your answer will depend on how you define your coordinate
system. Have your instructor or TA check your free body diagram and
Newton’s 2nd Law equations before going to step 7.
Copyright © 2001 Cummings; Rev. 2003 Bedrosian
7. Solving for acceleration: Use the relationships that you come up with in the step
above to solve for the acceleration of the cart during the time that the hanging mass is
falling. The acceleration expression should contain only the mass of the cart, the
hanging mass and the acceleration due to gravity. You must eliminate all other
variables from the expression, because we cannot measure (and do not know the
value of) these other variables.
8. Solving for the velocity of the cart after the block hits the floor: Combine the
expression for acceleration that you derived above and the expression for the velocity
of the cart that you derived as part of your homework. The result should be an
expression for velocity of the cart after the hang mass hits the floor that is a function
of ONLY: the mass of the cart, the hanging mass, the distance the hanging mass falls
and the acceleration constant of gravity (9.8 m/s2).
9. Exploration: Adjust the starting point of the cart so that you start at least a half of a
meter away from the motion detector. You will be measuring the velocity of the cart
after the hanging mass hits the floor but before the cart hits the end of the track. Is
the velocity of the cart constant during this time period? Why or Why Not? Choose a
mass for the hanging mass that allows the cart to achieve a reliably measurable
velocity before the hanging mass hits the floor. Please don’t let the cart smash into
the end stop on the track too hard. Record the mass of the cart (0.5 kg), the mass of
the hanging mass you will use, and the distance through which the mass will fall.
There is a “meter stick” on the low friction tracks that you are using – you can see
how far the hanging mass falls by subtracting the position of the cart when the
hanging mass hits the floor from the position of the cart at the point you will release
it. Use your expression for the velocity of the cart to determine what you think the
resulting velocity of the cart should be with the set-up you are using. Record that
value here and show all of your work in determination of it. Draw a sketch of what
you predict the velocity versus time and acceleration versus time graphs will look
like.
10. Making Experimental Measurements: Start LoggerPro. Then go File, Open, <Your
Physics1 Data Folder>, L01A2-1 (Velocity Graphs).mbl Use LoggerPro to measure
the velocity of the cart after the hanging mass hits the ground. Record that value.
Repeat the measurement at least once and record the second value. Be as accurate as
you can in determining the velocity from the LoggerPro graphs. For example, click
on the x=? icon at the top of the page point the cursor to the graph. Another way to
do this is to view the data table.
11. Comparing your predicted value with the measured values. Do the two values
agree? What is the percent difference between the two values ? What are the
limitations on the accuracy of your measurements and analysis?
Copyright © 2001 Cummings; Rev. 2003 Bedrosian