Physical Science Institute
Summer 2013
Acceleration Station
Teacher’s Guide
Materials per 3 person group:
1 cart
1 VERNIER dynamics System
1 pulley attachment
VERNIER LABQUEST2
1 hanging mass set including mass hanger
motion detector
These items are available from the following vendors:
Vendor
PASCO
PASCO
VERNIER
VERNIER
VERNIER
VERNIER
VERNIER
Item
Hanging Mass Set
String
LabQuest2
Pulley Bracket
Pulley Attachment
Dynamics system
Motion Detector
Item Number
ME-8979
SE-8050
LBQ2
B-SPA
SPA
VDS
MD-BTD
Experiment:
Set up your cart system so that the cart accelerates at a rate of 55  2
cm
sec .
sec
1. Include separate free-body diagrams for the cart and the falling mass. Be sure to label each force that is acting on
each object. Only diagram the forces in the direction of motion. Choose each object’s direction of motion as the
positive direction.
Force Diagram for Cart
Force Diagram for falling mass
Rope Tension
Friction
Rope Tension
Gravity
2. What did you do to the falling mass/cart system to get the desired acceleration? Name all variables and state what
your control, test variable, and outcome variables are for this exploration.
What was done to the falling mass/cart system to get the
desired acceleration?
Control
Test Variable
Outcome Variable
Added 27g to the falling mass
Mass of Cart which was 530 grams
Hanging Mass
Acceleration of Cart
3. If the cart accelerates at 55 cm/s2, what is the acceleration of the falling mass?
55 cm/s2
4. How do you think that increasing the cart mass while leaving the falling mass unchanged, would affect the
acceleration of the cart?
It would decrease the acceleration of the cart.
5. How do you think that increasing the falling mass while leaving the cart mass unchanged, would affect the motion of
the cart?
It will increase the acceleration of the cart.
6. Newton’s second law states that the sum of all of the forces acting along an object’s direction of motion equals the
product of the object’s mass and its acceleration. Assuming the tension force (FT), acting along the string that connects
the cart to the falling mass is the same for each object; write an equation for each separate object. Assume the force of
friction is negligible and do not include it. (Use your free body diagrams to determine which forces act along each
object’s direction of motion. Assign these forces a positive value.)
Newton’s 2nd law equation for the cart:
FT – Ffriction = Ma Ignoring friction gives FT = Ma
Newton’s 2nd law equation for the falling mass:
Fgravity – FT = ma
7. Is it possible to create a formula using the equations written above that predicts our outcome variable? Let’s try this
by using a system of equations. (Let m=mass of falling mass, and M=mass of cart, also use mg as the force of gravity)
Step 1: Using the equation you created for the falling mass
in question 6, solve for the tension in the string.
FTension = Fgravity - ma
Step 2: Substitute this result for the tension in the string
from the equation you created for the cart.
Fgravity – ma = Ma
Fgravity = Ma + ma
Step 3: Use algebra to solve for the acceleration.
mg = Ma + ma
mg = a(M+m)
a = mg/(M+m)
2
8. Plug your mass data from the experiment into this new equation and solve for a, using 9.8 m/s2 for g.
A = (0.027)(9.8)/(0.530 + 0.027) = 0.48 m/s2
How does this result compare with the result you obtained in the experiment?
It is less than the experimental value.
How can you account for the difference?
The theoretical solution assumes an ideal system in which there are no external forces. It also assumes perfect data. The
actual mass needed in the system will always vary from the theoretical solution.
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