Studio Physics I
Design Activity #1-Forces and Motion in 2 Dimension
The Problem:
You are a volunteer in the city’s children’s summer program. One suggested activity is
for the children to build and race model cars along a level surface. To ensure that each
car has a fair start, your co-worker recommends a special launcher be built. The launcher
uses a string attached to the car at one end and (after passing over a pulley) the other end
of the string is tied to a mass hanging straight down. The car starts from rest and the
block is allowed to fall, launching the car along the track. After the block hits the
ground, the string no longer exerts a force on the car but the car continues moving along
the track. You want to know how the launch speed of the car depends on the parameters
of the system that you can adjust. You decide to calculate how the launch velocity of the
car depends on the mass of the car, the mass of the hanging mass and the distance the
hanging mass falls.
In terms of these quantities, what is the velocity of the car after being
pulled by a given mass for a known distance?
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 of 1 kg), 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.
Homework/Preparation Questions:
All of the following questions should be written out on paper. You should bring that
paper with you to your next class. It will be the beginning of your activity write-up. In
addition, some of the answers will be entered into webassign as part of your homework as
well.
1. Make a sketch of the problem situation (equipment). Draw vectors which show
the direction and relative magnitude of the motion of the objects (both velocity
and acceleration) at the two interesting times in the problem: when the car stars
from rest and just before the block hits the floor. Draw vector to show all of the
forces on the hanging mass, the cart and the string. Assign appropriate symbols to
all of the quantities that describe the motion and the forces. If two quantities have
the same magnitude, use the same symbol but write down your justification for
doing so. For example, the car and the hanging mass have the same magnitude of
velocity. Explain why. Decide on your origin and coordinate system and draw it.
2. The known quantities in this problem are the mass of the hanging mass, the mass
of the car and the height of the hanging mass above the floor. Assign these
quantities symbols so that you can use them in algebra. The unknown quantity is
the velocity of the car and the hanging mass just before the block hits the floor.
There are other unknowns as well. List them. What is the relation between what
you really want to know (the velocity of the car after the block hits the floor) and
what you can calculate (the velocity of the car just before the block hits the
floor)?
3. Write down what principles of Physics you will use to solve this problem.
Because forces determine the motion of the car, using Newton’s 2nd Law to relate
the sum of the forces on each object and its motion is a good bet. We will do this
in class. For now, assume that you can find an algebraic expression for the
acceleration of the cart. Write down any kinematics equations that are
appropriate to this situation. You will have to decide if the acceleration each
object is constant or varies during the time interval for which your calculation is
valid. What is the time interval? Starting with the two basic equations of motion
with constant acceleration we have used in class so far, derive an expression for
the acceleration of the cart just after the hanging mass hits the ground in terms of
only the acceleration of the cart, the mass of the cart, the hanging mass, the
acceleration due to gravity and the distance that the hanging mass falls. Note that
you must have an expression that does not contain the time period.