DATA Experimenting with pendulums, you attach a light string to the ceiling and attach a small metal sphere to the lower end of the string. When you displace the sphere 2.00 m to the left, it nearly touches a vertical wall; with the string taut, you release the sphere from rest. The sphere swings back and forth as a simple pendulum, and you measure its period T . You repeat this act for strings of various lengths L , each time starting the motion with the sphere displaced 2.00 m to the left of the vertical position of the string. In each case the sphere’s radius is very small compared with L . Your results are given in the table: (a) For the Five largest values of L , graph T 2 versus L . Explain why the data points fall close to a straight line. Does the slope of this line have the value you expected? (b) Add the remaining data to your graph. Explain why the data start to deviate from the straight-line fit as L decreases. To see this effect more clearly, plot T / T 0 versus L , where T 0 = 2 π L / g and g = 9.80 m/s 2 . (c) Use your graph of T / T 0 versus L to estimate the angular amplitude of the pendulum (in degrees) for which the equation T = 2 π L / g is in error by 5%.
DATA Experimenting with pendulums, you attach a light string to the ceiling and attach a small metal sphere to the lower end of the string. When you displace the sphere 2.00 m to the left, it nearly touches a vertical wall; with the string taut, you release the sphere from rest. The sphere swings back and forth as a simple pendulum, and you measure its period T . You repeat this act for strings of various lengths L , each time starting the motion with the sphere displaced 2.00 m to the left of the vertical position of the string. In each case the sphere’s radius is very small compared with L . Your results are given in the table: (a) For the Five largest values of L , graph T 2 versus L . Explain why the data points fall close to a straight line. Does the slope of this line have the value you expected? (b) Add the remaining data to your graph. Explain why the data start to deviate from the straight-line fit as L decreases. To see this effect more clearly, plot T / T 0 versus L , where T 0 = 2 π L / g and g = 9.80 m/s 2 . (c) Use your graph of T / T 0 versus L to estimate the angular amplitude of the pendulum (in degrees) for which the equation T = 2 π L / g is in error by 5%.
DATA Experimenting with pendulums, you attach a light string to the ceiling and attach a small metal sphere to the lower end of the string. When you displace the sphere 2.00 m to the left, it nearly touches a vertical wall; with the string taut, you release the sphere from rest. The sphere swings back and forth as a simple pendulum, and you measure its period T. You repeat this act for strings of various lengths L, each time starting the motion with the sphere displaced 2.00 m to the left of the vertical position of the string. In each case the sphere’s radius is very small compared with L. Your results are given in the table:
(a) For the Five largest values of L, graph T2 versus L. Explain why the data points fall close to a straight line. Does the slope of this line have the value you expected? (b) Add the remaining data to your graph. Explain why the data start to deviate from the straight-line fit as L decreases. To see this effect more clearly, plot T/T0 versus L, where
T
0
=
2
π
L
/
g
and g = 9.80 m/s2. (c) Use your graph of T/T0 versus L to estimate the angular amplitude of the pendulum (in degrees) for which the equation
T
=
2
π
L
/
g
is in error by 5%.
Having successfully survived his first bungee jump, Ron is hanging at rest from the end of the bunjee cord. "I wonder what the spring constant of this bungee cord is?" he asks himself. So he decides to perform an experiment. He pulls himself up about 75cm and lets go. As he begins to bob up and down, he times his bounces and finds that he completes 4 oscillations in 20 seconds. He knows his mass is 75 kg.
a. What is the period of his motion?
b. What is the frequency of his motion?
c. What total distance dows he travel in 20 seconds?
d. What is the spring constant of the bunjee cord?
A ball with a mass of 240 g is tied to a light string that has a length of 2.80 m. The end of the string is tied to a hook, and the ball hangs motionless below the hook. Keeping the string taut, you move
the ball back and up until it is a vertical distance of 1.08 m above its equilibrium point. You then release the ball from rest, and it oscillates back and forth, pendulum style. As usual, we will neglect air
resistance. Use g = 9.80 m/s2.
(a) What is the highest speed the ball achieves in its subsequent motion?
m/s
(b) What is the maximum height the ball reaches in its subsequent motion (measured from its equilibrium position)?
(c) When the ball passes through the equilibrium point for the first time, what is the magnitude of the tension in the string?
N
After landing on an unfamiliar planet, a space explorer constructs a simple pendulum of length 55.0 cm . The explorer finds that the pendulum completes 109 full swing cycles in a time of 142 s .
How does one determine the magnitude of the gravitational acceleration on this planet, expressed in meters per second?
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