Question

One student set up the experiment to study the behavior of the pendulum, he did 6 trials, keeping the amplitude in 15 degree and changing the length of the pendulum, with a timing device he determines the period for different lengths. The experimental data is shown below,

trial	L[m]	T[s]
1	0.5	1.37
2	0.6	1.50
3	0.7	1.63
4	0.8	1.74
5	0.9	1.85
6	1	1.96

To examine more carefully how the period, T depends on the pendulum length , the student creates the graph T 2 vs L, and he noticed that the graph is practically a straight line.

1. What are the units of the slope? Explain, show your calculations
2. What will be the slope of the graph if the % error for g experimental is 3.06 %? Show your calculations
3. What will be the % error for g if the student uses the trial “3”, from the data table? show your calculations
4. What is the mass of the pendulum? Explain.

Answer 1

a)

we know

T = 2 sqrt ( L/g)

T² = 4² L / g

so,

slope of T² vs L graph is ( 4² / g ) where 4² is unitless and g has units of m/s²

so,

units of slope are s² / m (please note that question asks units of slope, not g)

___________________________

b)

standard value for g = 9.8 m/s²

% error = 3.06 %

we know

% error = ( theoretical value - experimental value ) \ ( theoretical value) * 100

0.0306 = 9.8 - experimental value / 9.8

experimental value = 9.5 m/s²

however, the questions asks for value of slope

so,

slope = 4² / g

slope = 4.155

_____________________

c)

using trail 3,

1.63² = 4² * 0.7 / g

g = 10.4 m/s²

so,

% error = 10.4 - 9.8 / 9.8 * 100

% error = 6.122 %

_________________________________

d)

The mass cannot be found with given info....even if we 15 degree angle to find the releases height and then use conservation of energy, the mass will eventually cancel out.