Part 3 – Angle of release
- Repeat steps 1 to 6 from part 1 using a 100g mass.
- Adjust the angle of release such that it is 180 degrees from the horizontal.
- Release and record time of one period.
- Repeat with the same angle using 195, 210, 225, 250 degrees from the horizontal.
- Perform five trials and calculate the average period.
DATA AND OBSERVATIONS:
Table 1 – The affect of mass of weight on period
(Note: length of rope is 30cm; angle is release is 180° from the horizontal)
Table 2 – The affect of length of string on period
(Note: mass of weight is 100g; angle is release is 180° from the horizontal)
Table 3 – The affect of angles on period
(Note: mass of weight is 100g; length of rope is 30 cm)
OBSERVATIONS:
Graph 1, 2, 3, and 4 attached.
All slopes, equations, and error bars included.
ANALYSIS:
Graph 1 – Average time tavg (s) vs. Mass m (g)
- Shape: curve
- Slope: unable to determine due to shape
- Y-intercept: unable to determine
- Equation: unable to determine
- Error barsY (justification provided under SOURCES OF UNCERTAINTY): ±0.05s
- Error barsX (justification provided under SOURCES OF UNCERTAINTY): ±0.01g
Graph 2 – Average time2 t2 (s2 ) vs. Mass m (g)
- Shape: curve (theoretically a line)
- Slope:
-
∆t2 / ∆m
-
= 0.275s2 /300.00g
-
= 2.54x10-4 s/g
- Y-intercept: 0s
- Equation:
-
y= t2
-
m= 2.54x10-4 s/g
- x= m
- b=0s
-
t2= 2.54x10-4 s/g (m) + 0s
-
t= ±√(2.54x10-4 s/g (m) + 0s)
Looking at Graph 2, we can observe a gradual relationship between the mass and average period of pendulum motion. This observation, although contrary to my hypothesis, is an accurate representation of a realistic pendulum motion. Almost any experiment will have air resistance, or friction, that will slow down objects with a large drag. As shown in Graph 2, heavier and more air resistant weights take longer to complete a period because it takes the weights longer time to push through air molecules. In theory, mass should not affect the motion of a pendulum because gravity is the same for all objects on earth, as defined by Newton’s second law of motion F=ma and the gravitational acceleration on earth (9.8m/s/s); however, there is air friction in reality so as the mass increases, the period increases slightly as well.
Graph 3 – Length l (cm) vs. Average time t (s)
- ∆l/∆tavg
- =17cm/0.35s
- =49cm/s
- Y-intercept = 6cm
- Equation:
- y= l
- m=49cm/s
- x=tavg
- b=6cm
Looking at Graph 3, we can observe a direct and proportional relationship between the length of string and average period of pendulum motion. As I hypothesized, the length the string in pendulum motion will affect the average period because the length affects the amount of distance the weights have to travel before completing one round trip, or a period. If the distance has increased and the acceleration has not, it would make sense to say that a longer string would increase the period since the object has to cover a longer distance. If a= v/t, v=d/t, a=d/t/t, and the acceleration remains constant, whenever the distance is increased the time it takes is also increase, and vice-versa. The length of string is directly related to the period of pendulum motion.
Graph 4 – Angle a (degrees °) vs. Average time tavg (s)
- ∆a/∆tavg
- =75°/0.33s
- =230°/s
- Y-intercept: 255°
- Equation:
- y= a
- m= 233°/s
- x= tavg
- b=255°
Looking at Graph 4, we can observe a direct and proportional relationship between the angles of release and the average period, similar to that of Graph 3. As I hypothesized, the angle of release directly affects the average period because as the angle comes closer to the vertical the object has less distance to travel in a period. And when the distance an object travels is decreased without changing the acceleration, period is decreased. Similar to the explanation to Graph 3, when the distance is decreased (angle approaching 270°) and acceleration remains constant, the time it takes for one period is also decreased. Therefore, the angle of release and the average period of a pendulum motion are directly related.
CONCLUSIONS:
There is a proportional relationship between length of string and the period as represented by the equation l= 49cm/s (T) + 6cm, where l is the length, T is the period, and a line is produced. There is a proportional relationship between the angle of release and the period as represented by the equation a= 233°/s (T) + 255°, where a is the acceleration, T is the period, and a line is produced. Theoretically, there is no relationship between the mass and the period; however, since there is air resistance in the laboratory, large objects have bigger drag and take longer to complete one period. The equation T= ±√ (2.54x10-4 s/g (m) + 0s) represents the length of the period as a function of the mass; as we can see from the equation, the mass will not have a significant impact on the period of the pendulum motion.
There is no accepted value for this design lab; therefore, it is inappropriate to designate an arbitrary value to compare to my measured value.
SOURCES OF UNCERTAINTY:
- human error (timing, angles, length of string)
- timing – ±0.5s (biggest difference out of 5 values)
- angles - ±5° (protractor was accurate but it was sometimes hard to read)
- length of string - ±3cm (we measured the specified length of string before taping and tying the rope, creating room for error)
- negligible, but clearly relevant in Graph 1 and Graph 2
- friction in the ring clamp
- the curved shape of the clamp
- I chose to record each period separately as opposed to dividing a total number of periods by its swings because I believe that he extra swings would bring in many unknown factors into the system such as momentum. By recording each swing separately, I can make sure that each swing is clean and the weights will not sway or jump. However, multiple timings can create more room for error; therefore I made up for the lost accuracy by increasing my uncertainty in timing.