Problema Solution
Simple Pendulum Gravity is responsible for an object falling toward Earth. The farther the object falls, the faster it is moving when it hits the ground. For each second that an object falls, its speed increases by a constant amount, called the acceleration due to gravity, denoted g. One way to calculate the value of g is to use a simple pendulum.
The time T for a pendulum to swing back and forth once is called its period and is given by
(a) Solve the formula for g.
(b) Use the table to determine the value of g. (Note: The units for g are feet per second per second.)
(c) Interpret your result.
T = 2π√L/G
where L equals the length of the pendulum. The table lists
the periods of pendulums with different lengths.
L (feet) 0.5 1.0 1.5
T (seconds) 0.78 1.11 1.36
Answer provided by our tutors
The time T for a pendulum to swing back and forth once is called its period and is given by
T = 2π √ L/g
where L equals the length of the pendulum. The table lists the periods of pendulums with different lengths.
L(feet)............. 0.5...........1.0..........1.5
T(seconds)..... 0.78.........1.11........1.36
(a) Solve the formula for g.
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T = 2π √ L/g
sqrt(L/g) = T/(2pi)
L/g = [T/(2pi)]^2
g = L/[T/(2pi)]^2
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(b) Use the table to determine the value of g. (Note: The
units for g are feet per second)
Using the point (1,1.11), solve for "g":
g = 1.11/[1/(2pi)]^2
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g = 1.11*4(pi^2)
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g = 43.821 ft/sec
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(c) Interpret the result.
The force of gravity on the pendulum is 43.821 ft.sec