John walks four kilometers east, two kilometers north as shown in the diagram below. What is John’s displacement
2 answers:
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The period of a simple pendulum is given by:
where L is the pendulum length, and g is the gravitational acceleration of the planet. Re-arranging the formula, we get:
(1)
We already know the length of the pendulum, L=1.38 m, however we need to find its period of oscillation.
We know it makes N=441 oscillations in t=1090 s, therefore its frequency is
And its period is the reciprocal of its frequency:
So now we can use eq.(1) to find the gravitational acceleration of the planet:
where L is the pendulum length, and g is the gravitational acceleration of the planet. Re-arranging the formula, we get:
We already know the length of the pendulum, L=1.38 m, however we need to find its period of oscillation.
We know it makes N=441 oscillations in t=1090 s, therefore its frequency is
And its period is the reciprocal of its frequency:
So now we can use eq.(1) to find the gravitational acceleration of the planet:
To solve this problem it is only necessary to apply the kinematic equations of angular motion description, for this purpose we know by definition that,
Where,
Angular Displacement
Angular Acceleration
Angular velocity
Initial angular displacement
For this case we have neither angular velocity nor initial angular displacement, then
Re-arrange for
Replacing our values,
Therefore the ANgular acceleration of the mass is