Concept of the experiment

Two masses slung over a pulley,
linked through a string of
negligible mass.

Since they are linked by string,
they have the same magnitude
of acceleration, with heavier mass
moving downwards and
lighter mass moving upwards.

Theoretical acceleration: Free body diagram

Key Idea: Draw each of the bodies separately, detached from
the system, and draw all forces acting on it to find resultant
force, and hence, resultant acceleration.

Deriving the equation for m2

For m2 :

Acceleration is upward
Net force is upward
Magnitude of tension is bigger than magnitude weight of m2
So equation is:
T − m

2
g= m

2
a → T = m

2
g + m

2
a . (1)

Deriving the equation for m1

For m1 :

Acceleration is downwards
Net force is downwards
Magnitude tension is smaller than magnitude weight of m1
So equation is:
m
1
g − T = m

1
a . (2)

Deriving the equation for acceleration a

Solving for acceleration a:

Substituting tension from (1) into (2), we get:

m
1
g −m

2
g − m

2
a = m

1
a

→ a =
m
1
− m

2

m
1
+ m

2

g (3)

NOTE: We use the values we get from this equation as the
accepted values for computing the % errors in Table 1.

Outline of procedure

We will taking different values of masses for m1 and m2 and
releasing the heavier mass to measure the acceleration.

In order to do so, we measure the change of velocity of the
mass over time and then plot magnitude of velocity versus time,
with the help of the computer. Then, we find the acceleration from
the slope of the plot.

v

t

Slope
→ acc.

Provided data for Exp 5 and instructions for data analysis and lab report

1. Provided fitting data for Exp 5 are given in Fig. 1 in which the #’s correspond to the Measurement #.

Measurement #1:
1m = 0.060 kg,

2m = 0.050 kg

Measurement #2:
1m = 0.060 kg,

2m = 0.040 kg

Measurement #3:
1m = 0.055 kg,

2m = 0.045 kg

Measurement #4:
1m = 0.065 kg,

2m = 0.035 kg

2. Instruction for data analysis

(a) Determine (exp.)a from the fitting parameters shown in Fig. 1.

Record (exp.)a with its units in Table 1.

(b) Calculate
(3)( .)calca from Eq. (3) using the values of

1m and
2m listed in column 1 of Table 1.

Record
(3)( .)calca with its units in Table 1.

Attention: Point deduction will be given to your report if the recorded data have no units.

(c) Calculate the percentage error between (exp.)a and
(3)( .)calca .

Record the % error in Table 1.

(#1)

(#3)

(#2)

(#4)

Figure 1 Plots and fittings of data from the 4 measurements in Exp 5

Table 1 Comparison of (exp.)a with
(3)( .)calca

Measurement

Masses (kg)

Slope (exp.)a

(3)( .)calca

% error between

(exp.)a and
(3)( .)calca

Measurement #1

1
m = 0.060,

2
m = 0.050

Measurement #2

1
m = 0.060,

2
m = 0.040

Measurement #3

1
m = 0.055,

2
m = 0.045

Measurement #4

1
m = 0.065,

2
m = 0.035

3. Instructions for lab report

(a) Tables 1 with all the analyzed data and units must be included in your Exp 5 lab report.

(c) Answers to the 4 questions at the end of Exp 5 lab manual must be included in your Exp 5 report.

(d) The required other contents and format for your lab report can be found in the syllabus.