Discussion and review A pendulum is a weight hanging from a fixed point so that it swings freely under the combined forces of gravity and momentum

Subject:PhysicsPrice:3.86 Bought7

Share With

Discussion and review

A pendulum is a weight hanging from a fixed point so that it swings freely under the combined forces of gravity and momentum. A simple pendulum consists of a heavy pendulum bob (of mass M) suspended from a light string. It is generally assumed that the mass of the string is negligible. If the bob moves away from the vertical to some angle θ, and is released so that the pendulum swings within a vertical plane, the period of the pendulum is given as:  T = 2π 

symbol

Description

T

Period of a pendulum to complete one cycle

L

Length of string

g

Acceleration due to gravity: 9.81 m/s²

Procedure

The lab activity uses a simulation developed by the University of Colorado at Colorado Boulder. 

Simple Pendulum Click here

1.     The length 1 of the pendulum should be set to the following approximate lengths: 0.25 m - 1.00 m in 0.25 m increments.

2.     For each length, set the pendulum in motion by displacing the pendulum bob an angle less than 10⁰ from the vertical.

3.     Start timer when strings appear to be aligned. Wait for next alignment and count first oscillation, the next alignment will be the second oscillation and so on. Count out a total of 10 oscillations and stop timer precisely on the 10^thoscillation. Record the total time elapsed for the 10 oscillations.

4.     Repeat the previous step a total of 3 times.

5.     Divide each of the times by 10 and then square them to get the Period squared.

6.     Find the average  and the standard deviation. With careful measurement it should be possible that the standard deviation is less than 1% of average  value.

Length

(m)

time [Trial 1]

(S)

time [Trial 2]

(S)

time [Trial 3]

(S)

t_avg

T = t_avg/10

T²

1.00 m

0.75 m

.50 m

0.25 m

Analysis

Hint:  is valid if the angular displacement from the equilibrium position is less than 10⁰

1.     Enter the lengths in one column and the average  in another column and the standard deviation of  in another column.  Include units at top of column.

2.     Make an xy scatter plot of  vs L

a.     Title

b.     Axes labels with units! [Please use graphing paper or excel for graph]

3.     What should the slope of the fit line be? How could you determine g from it?

4.     Using the slope of graph and calculated g.

5.     Solve Then calculate your percentage error as compared to the accepted value for g, which is 9.81 m/s². 

% error = [experimental value - theoretical value]  × 100

theoretical value