Measuring Force and Acceleration
A Scientific Investigation
Conducted by DJ Skittles and Witty Witch
(peerreviewed by DJ Hadoken)
Objective:
The objective of this scientific investigation is to observe the accelerations produced by varying forces on a given mass.
Materials:
A. 1 kg cart
B. Set of metric masses
C. Stopwatch
D. Pulley
E. String
F. Meterstick
G. Witty Witch’s hand
Procedure:
1. Load cart with the following masses: 50g, 100g, 200g. Attach one end of a long string to the cart. Pass the string over the pulley.
2. Remove the 50g weight from the cart and place it on a loop at the end of the string. Time the cart’s movement for one second and record measurements of distance, etc.
3. Remove the 100g weight from the cart and place it on a loop at the end of the string (remember to place the 50g one back on the cart). Time the cart’s movement for one second and record measurements of distance, etc.
4. Repeat the above steps for 150g, 200g and 250g masses and record measurements of distance, etc.
5. Do several trials and obtain the averages. Graph and analyze results.
Results:
Conclusion:
This experiment taught us the relationships between force, mass and acceleration. After completing all the investigations, the first graph was imagined, which shows the Time in seconds versus the Velocity in m/s2. In order to obtain this velocity, we kept the time constant (one second) and measured the distance traveled by the cart after the weight at the end of the string was released.
We used the formula d=Vit+(at2)/2, where d=distance, Vi= initial velocity=0 [since the cart starts from rest], a=acceleration, and t=time, to obtain acceleration. Once we obtained the acceleration, we were able to find the final velocity by using the formula Vf=Vi+at (where Vf=final velocity, and the rest of the variables are the same as in the previous equation).
The graph is thus a representation of two main points for each trial. For example, Trial #1 used the following two points: the velocity at time 0= (0,0), and the velocity at 1 second: (1, 0.86). The slope of this line is the acceleration, or 0.86 m/s2. In addition, if a line is drawn that connects the xaxis at 1 second to the line of time vs. velocity, the resulting area (area under the curve) of the triangle is the distance traversed by the cart, or in Trial # 1, 0.43 m.
The second graph (which you must imagine for yourself) ties together the experiment by looking at Force as the independent variable. The forces of the different trials are given to us and we must plot them against the slopes of the lines from the previous graph, or the accelerations. In doing this, we discover that the greater the force, the greater the acceleration. This supports Newton’s Second Law (though in a somewhat indirect way) because instead of varying the total weight of the system, it remained constant throughout the experiment (1.35 kg).
In conclusion, the blue highlighter that connects the 5 different points shows a pretty accurate representation of the differences in acceleration due to increasing forces. It is not a completely straight line (since all experiments are not perfectly accurate), but it is substantially correct.
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