A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below. Height of bob above floor (mm) Time for 50 oscillations (s) 400 155.3 600 148.8 800 142.2 1000 134.0 1200 127.4 1400 119.2 1600 110.5 The period T of the pendulum of length ℓ is given by ? = 2?√ℓ /? where ? is the acceleration due to gravity. But ℓ = ? − ℎ where ? is the height of the ceiling and h is the height of the centre of the pendulum above the floor. Therefore ? = 2? [(? − ℎ)/?]^1/2 Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that ? = 9.8 m s^2 (? could be obtained from the slope of the graph). Having obtained your values for H, answer the following questions: a) Which value of H do you consider to be the least accurate? Give reasons for your choice and explain how the accuracy could have been improved. b) Why was the bob set swinging through a small angle? c) Why was h measured to the centre of the bob? d) Why was the completed number of oscillations chosen to be large? e) Can you see any advantage in measuring the height of the ceiling in this way?
A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different
lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below.
Height of bob above floor (mm) Time for 50 oscillations (s)
400 155.3
600 148.8
800 142.2
1000 134.0
1200 127.4
1400 119.2
1600 110.5
The period T of the pendulum of length ℓ is given by
? = 2?√ℓ /? where ? is the acceleration due to gravity. But ℓ = ? − ℎ where ? is the height of the ceiling
and h is the height of the centre of the pendulum above the floor. Therefore
? = 2? [(? − ℎ)/?]^1/2
Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that ? = 9.8 m s^2 (? could be obtained from the slope of the graph). Having obtained your values for H, answer the
following questions:
a) Which value of H do you consider to be the least accurate? Give reasons for your
choice and explain how the accuracy could have been improved.
b) Why was the bob set swinging through a small angle?
c) Why was h measured to the centre of the bob?
d) Why was the completed number of oscillations chosen to be large?
e) Can you see any advantage in measuring the height of the ceiling in this way?
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A student was supplied with a stop watch, two metre rules and a simple pendulum suspended from a ceiling and was asked to measure the height of the ceiling indirectly. He set the pendulum swinging through a small angle and measured the period of oscillation for different
lengths of the pendulum. Since he was unable to measure the length of the pendulum directly, he measured the height of the centre of the pendulum bob above the floor. He obtained the results tabulated below.
Height of bob above floor (mm) Time for 50 oscillations (s)
400 155.3
600 148.8
800 142.2
1000 134.0
1200 127.4
1400 119.2
1600 110.5
The period T of the pendulum of length ℓ is given by
? = 2?√ℓ /? where ? is the acceleration due to gravity. But ℓ = ? − ℎ where ? is the height of the ceiling
and h is the height of the centre of the pendulum above the floor. Therefore
? = 2? [(? − ℎ)/?]^1/2
Plot a suitable graph to find the height of the ceiling H from the two intercepts using linear regression to fit the best straight line through the data points. Assume that ? = 9.8 m s^2 (? could be obtained from the slope of the graph). Having obtained your values for H, answer the
following questions:
a) Which value of H do you consider to be the least accurate? Give reasons for your
choice and explain how the accuracy could have been improved.
b) Why was the bob set swinging through a small angle?
c) Why was h measured to the centre of the bob?
d) Why was the completed number of oscillations chosen to be large?
e) Can you see any advantage in measuring the height of the ceiling in this way?
MAY I HAVE ANSWER FOR A TO E
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