Simple Pendulum: Gravity is responsible for an object falling toward Earth. The

Question

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.
See the accompanying figure.

t=2L/G

The time T for a pendulum to swing back and forth
once is called its period and is given by
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 (Time) 0.78 1.11 1.36

(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.

Explanation / Answer

(a) Solve the formula for g.

Given t=2L/G
or

t^2 = 4*pi^2 *L/g

or

g = 4*pi^2 *L/t^2 (Answer)

(b) Use the table to determine the value of g. (Note: The
units for g are feet per second per second.)

L (Feet) 1.0 T (Time) 1.11
Since g is constant takeing the value from the table and plugginh in :

g= 4*pi^2*1^2/(1.11)^2

solving g= 32.0090901712 ft/s^2 (Answer)

(c) Interpret your result.

The velocity of an object increases by 32 ft/s

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