Simple Pendulum Motion and Physical Pendulum

In summary, the period of a pendulum can be calculated using the formula P = 2*pi*sqrt(L/a), where L is the length of the arm and a is the acceleration. In the case of a stationary elevator or an elevator moving at a constant speed, only the acceleration due to gravity is taken into account. However, in situations where the elevator is accelerating, such as in (c) and (e), the total acceleration will be a combination of the acceleration due to gravity and the acceleration of the elevator. This will affect the value of 'a' in the formula and thus, the period of the pendulum.
  • #1
danield
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Homework Statement


1) Find the period of a pendulum 50 cm long when it is suspended in (a) a stationary elevator; (b) an elevator falling at the constant speed of 5.0 m/s; (c) an elevator falling at the constant acceleration of 2.0 m/s2; (d) an elevator rising at the constant speed of 5.0 m/s; (e) an elevator rising at the constant acceleration of 2.0 m/s2.

Homework Equations


Period = 2 pi Squareroot of Length of arm/ Gravity

The Attempt at a Solution


1) I could solve a) by simply replacing data into the formula, but I am not sure how does the change in velocity and acceleration affects the data that is where I am stuck at.
 
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  • #2
A force has to be introduced to change the period.

Constant motion doesn't introduce force, only acceleration does.
 
  • #3
so that means that when the velocity is up or down 5m/s constat there is no acceleartion, so only G is taken into account?
but for the toher two, how are they calculated?
 
  • #4
Gravity is an acceleration... the period is actually

P = 2*pi*sqrt(L/a)

where a is acceleration.

Gravity is always there, but in acceleration situations a will not simply be equal to G as it is in the stationary and constant motion situation.
 
  • #5
Yes i understand that part, but what i don't know is how does the up and down acceleration influence the total acceleration, this is just a hunch but i think that when acceleration is downward i would be 7.81, and when it is upward it will be 11.81, I am not totally sure about that
As for the ones where velocity is constant i think that the only acceleration acting is gravity, and I am not sure of that either..
 
  • #6
You are correct. The acceleration of the elevator adds (or subtracts) from the standard acceleration due to gravity (9.81 m/s^2).
 
  • #7
ok thanks very much
 

1. What is a simple pendulum?

A simple pendulum is a weight attached to a string or rod suspended from a fixed point. The weight is able to swing back and forth under the influence of gravity.

2. What factors affect the period of a simple pendulum?

The period of a simple pendulum is affected by the length of the string and the acceleration due to gravity. It is also affected by the angle at which the pendulum is released, but to a lesser extent.

3. How is the period of a simple pendulum calculated?

The period of a simple pendulum can be calculated using the equation T = 2π√(L/g), where T is the period, L is the length of the string, and g is the acceleration due to gravity.

4. What is a physical pendulum?

A physical pendulum is a rigid object suspended from a fixed point that is able to swing back and forth under the influence of gravity. Unlike a simple pendulum, a physical pendulum has a mass that is distributed throughout its body, rather than being concentrated at a single point.

5. How is the period of a physical pendulum calculated?

The period of a physical pendulum can be calculated using the equation T = 2π√(I/mgd), where T is the period, I is the moment of inertia of the pendulum, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance from the pivot point to the center of mass of the pendulum.

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