# Calculating the Acceleration of a Simple Pendulum

• corey2014
In summary, the pendulum has a maximum speed of 9.287 m/s when its amplitude is at 0.5 and when its displacement is at A.

## Homework Statement

A simple pendulum has a length of 4.9 m and is pulled a distance y = 0.5 m to one side and then released.

(a) What is the speed of the pendulum when it passes through the lowest point on its trajectory?

(b) What is its acceleration when it passes through the lowest point on its trajectory?

## Homework Equations

I think this is the equation I am supposed to use? omega=sqrt(2(9.8)(L(1-cos(a))) where omega is velocity max and L is length of pendulum, a is angle between Pendulum and its starting position

Not totally sure what to do with equations...

## The Attempt at a Solution

I tried solving for a and I got 1.262896 radians
then a final speed of 9.287 m/s

corey2014 said:

## Homework Statement

A simple pendulum has a length of 4.9 m and is pulled a distance y = 0.5 m to one side and then released.

(a) What is the speed of the pendulum when it passes through the lowest point on its trajectory?

(b) What is its acceleration when it passes through the lowest point on its trajectory?

## Homework Equations

I think this is the equation I am supposed to use? omega=sqrt(2(9.8)(L(1-cos(a))) where omega is velocity max and L is length of pendulum, a is angle between Pendulum and its starting position

Not totally sure what to do with equations...

## The Attempt at a Solution

I tried solving for a and I got 1.262896 radians
then a final speed of 9.287 m/s

Hopefully the question had a diagram with it, which will enable you to answer the following question: Was the 0.5 m the length of the arc along which the bob was drawn back, or is it the horizontal distance to the side, that the bob is drawn?

Use the work energy theorem.

There is no diagram but because it says y= can't I assume that its in the Y direction? And what is that theorem?

I think it means the horizontal distance it is displaced, the work energy theorem says that the total change in kinetic energy of an object is equal to the sum of the work done on that object. In this case the work done by gravity in going from the highest position to the lowest is equal to the kinetic energy at the lowest (since its speed was 0 in the highest position).

This is a problem about Simple Harmonic Motion (SHM)
A simple pendulum can be assumed to perform SHM.
The amplitude, A, of the motion is 0.5m.
The Time period and therefore the angular velocity can be found from the pendulum equation
T =2∏√l/g, ω=2∏/T
In SHM max velocity occurs when amplitude = 0 and is given by ωA
Acceleration when amplitude = 0 is ZERO
Max acceleration = ω^2 A and occurs when displacement = A

All of this makes the usual assumptions about a simple pendulum... small angle etc.

## What is a simple pendulum?

A simple pendulum is a system consisting of a mass attached to a string or rod that is suspended from a fixed point. When the mass is pulled to one side and released, it will swing back and forth in a regular pattern.

## How do you calculate the acceleration of a simple pendulum?

The acceleration of a simple pendulum can be calculated using the equation a = -(g/L)sinθ, where a is the acceleration, g is the acceleration due to gravity (9.8 m/s²), L is the length of the pendulum, and θ is the angle of the pendulum from its resting position.

## What factors affect the acceleration of a simple pendulum?

The acceleration of a simple pendulum is affected by its length, mass, and the force of gravity. The longer the pendulum, the smaller the acceleration. The heavier the mass, the greater the acceleration. The force of gravity also plays a role, as it determines the value of g in the acceleration equation.

## How does the angle of the pendulum affect its acceleration?

The acceleration of a simple pendulum is directly proportional to the sine of the angle of the pendulum. This means that as the angle increases, the acceleration also increases. However, this relationship is only true for small angles. As the angle approaches 90 degrees, the acceleration decreases and becomes zero at 90 degrees.

## Can the acceleration of a simple pendulum ever be greater than the acceleration due to gravity?

No, the acceleration of a simple pendulum can never be greater than the acceleration due to gravity. This is because the acceleration due to gravity is a constant value and the acceleration of the pendulum is dependent on other factors, such as length and mass. However, the acceleration of the pendulum can be equal to the acceleration due to gravity when the angle of the pendulum is 90 degrees.