Bob Somers
11/3/04
Per. 4
Lab Partners: Megan Van Matre, Mark Saenger
Force and Acceleration of Systems
Purpose
The purpose of this lab was to determine whether or not there was a linear relationship (in
the form of a ratio) between the force applied on an object and its acceleration. We could
determine this using the supplied apparatus with minimal calculations
Theory
The theory behind this lab was that we could use the force of gravity to propel a system
and measure its acceleration to draw a conclusion regarding the force applied and the
system’s acceleration. Supposedly, the force applied and the resultant acceleration from
the force applied are directly proportional, meaning that they not only increase and
decrease together but that they do so at a constant rate. Using measured acceleration from
the computer probes and our force of gravity calculations we could determine how much
force is actually being applied on the system and therefore the relationship between force
and acceleration.
Procedure
1. Place 100g of mass in the form of one 50g mass, two 20g masses, and one 10g
mass onto the tray of the dynamics cart.
2. Make sure the computer equipment and velocity/acceleration probe is correctly
configured and making correct readings.
3. Move the 10g mass from the tray of the dynamics cart to the end of the paperclip.
4. Pull back the dynamics cart and prepare the computer for data logging.
5. Start data logging and release the dynamics cart. If readings on the computer seem
mostly error-free, proceed to next step. Otherwise re-run trial making minor
adjustments to the computer equipment and velocity/acceleration probe until you
get the desired readings.
6. Change the velocity vs. time graph to reflect acceleration vs. time and use the
computer software to approximate the constant rate of acceleration experienced
by the dynamics cart.
7. Record the data and continue the trails from steps 3 through 7 successively
swapping out larger masses for smaller ones, but keeping the mass of the system
constant at 100g.
Data
Trial
1
2
3
4
5
Mass (in g)
10
20
30
40
50
Acceleration (in m/s2)
0.148
0.308
0.468
0.627
0.788
Observations
• The dynamics cart moves very freely, as if almost frictionless.
• The larger the mass, the faster it pulls the dynamics cart.
• The computer software is prone to mistaken readings.
• There is a very short distance over which to gather data.
• If you don’t catch the cart, it rebounds with almost exactly as much force at which
it was initially pulled at.
Calculations
Using the force of gravity formula, we calculate the exact force exerted on the system.
Since we can assume that the environment was frictionless, we can assume that the force
of gravity was the only force acting upon the system.
Fg = mg
Fg = (10g)(9.80m/s2)
Fg = 0.098 N
By similar method, we compute the rest of the forces acting upon the rest of the masses.
Fg = (20g)(9.80 m/s2) = 0.196 N
Fg = (30g)(9.80 m/s2) = 0.294 N
Fg = (40g)(9.80 m/s2) = 0.392 N
Fg = (50g)(9.80 m/s2) = 0.490 N
Next we find the slope of the line of best fit. This will be our common ratio between
force and acceleration. Using two of the data points that landed on the line we obtain:
m = y2 – y1
x2 – x1
m = 0.392 – 0.196
0.627 – 0.308
m = 0.614
Error Analysis
There were several possible sources of error in this lab. First of all, the dynamics cart was
not frictionless, even though we operated under the assumption that is was. Second, the
computer probes were not entirely accurate, given that they took quite a bit of
configuration before they even gave readings in the ballpark of possible answers. Third, it
is always possible than kinks in the line or jerks on the line as the mass was descending
could cause irregular acceleration, skewing the acceleration graph slightly and therefore
the number derived from it by the computer.
Conclusion
The attached graph suggests that our assumption was correct, that the force applied to and
the acceleration of an object are directly proportional, with a common ratio of 0.614. The
resultant units are Newtons per meter per second squared. This may suggest that the
graph is inferring about the amount of work done in the problem. The common ratio
between force and acceleration is how many Newtons it pushes in how many meters it
travels and in how many seconds (squared, of course) it does this. One could easily
perceive the graph as a definition of the work that an object did.