Accelerating Two Masses
(Walter Fendt Simulation)
Period
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Table
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Group
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Introduction: This lab activity is
intended to provide additional
experience with Newton’s second
law. The basic laboratory set up is
shown in the figure below where a
frictionless cart is pulled on a
horizontal surface by a weight
hanging over the edge of the table.
The simulation screen is shown on
the right below. In the simulation, the
acceleration of the cart is measured
by timing the known distance the cart travels. This arrangement can be considered as
two separate masses moving in two different directions (horizontal and vertical) with one
mass pulling the other and joined by a string transferring the force from one to another.
However the analysis can be simplified by considering that both masses move together
as a single system reducing the motion to a single dimension. This motion is that of a
single system with mass equal to the total mass being accelerated. In this analysis, the
string tension is an internal force and thus is not part of the analysis to find the
acceleration of the system. If the tension in the string is known, it can be considered as
an external force to each of the accelerating masses and Newton’s second law checked
for that particular mass (cart or hanging mass). In this experiment we do not know the
tension in the string but can compute it if desired.
Materials: Computer with internet connection or with the simulation loaded
http://www.walter-fendt.de/ph14e/n2law.htm.
Procedure:
1. Run the simulation and set the coefficient of friction to zero, set the mass of the
wagon (M) to 1000 g and the mass of the hanging mass (m) to 100 g.
2. Push Start and allow the simulation to proceed. Read the acceleration value from
the screen and record in the proper place on the laboratory report.
3. Change the wagon mass (M) to a value of 500 g and repeat step 2.
4. Fill in the remaining blanks and answer the questions on the Lab Report.
Accelerating Two Masses (Lab Report)
Motion of Total System:
Trial
M (kg)
m (kg)
M+m (kg)
mg = Force (N)
1
1 kg
0.1 kg
1.1 kg
.98 N
2
0.5 kg
0.1 kg
a (m/s2)
Create a free-body diagram of the entire system of two masses with the motion represented in
the “x” direction. The sketch of the two-mass system below should guide your diagram.
Analysis: The net external force on this total system is the weight of the hanging mass. The
total mass being accelerated is the mass of the wagon and the hanging mass. For the second
trial compare the total mass times the acceleration with the accelerating force.
Total mass times acceleration: (M+m)a ____________________ N
Weight of hanger: mg ________________________ N
How do these two values compare? ____________________________________
Motion of Wagon as a System: Use the second trial above as an example calculation
1. Consider the wagon as a separate system and the hanging mass as a
separate system. The free-body diagram for the hanging mass is shown.
Use that diagram to calculate the tension in the string.
Tension
mg
2. Create a free-body diagram for the wagon and, knowing the tension force from above;
calculate the acceleration of the wagon. Compare this to the measured value.