ElbatnigiD_Lab5

Carleton University Laboratory Report Course #: Experiment #: Simple Pendulum Lab Doua Elbatnigi 101101462 Date Performed: November 22 nd , 2022 Date Submitted: November 29 th , 2022 Lab Period: L1 Partner: Joanna Station #: 38 TA: Raad

Purpose The purpose of this lab is to determine the relationship between the period of a pendulum and different parameters. We will also use our knowledge to determine the pendulum’s conservation of energy. Observations/Graphs Bob Color Material Mass: ( m±σ m ) units Diameter ( d ±σ d ) units 1 Copper- yellow Brass 47.99 ± 0.01 19.07 ± 0.01 2 Light grey without rust Aluminum 13.93 ± 0.01 19.07 ± 0.01 Figure 1.0: Data Table representing the color, material, mass, and diameter of Bob 1 and 2. Bob used in Part 2 Average Period from Acquisition File T σ SD N σ mean 10 8.952 6 1.178 ∴ ( T ±σ mean ) units = 10±1.178 Interpolated Period from Analysis File L L − σ L L + σ L 35.7 35.6 35.8 T i T 1 at L − σ L T 2 at L + σ L 1.1858 1.1842 1.1875 ∴ ( T i ±σ T i ) units = 1.1858 ± 0.00165 Figure 2.0: Data Table showing the average period of….. and interpolated period

Calculations Use templates from previous labs to copy/paste any symbols or equations that you may require to complete this report. Below are all the equations from the Theory section of the Lab Manual. They may or may not be needed to complete the required calculations. θ 0 = sin − 1 ( x L ) θ ( t ) = θ 0 cos ( 2 πt T ) T ≈ 2 π √ L g T = 2 π √ L g ( 1 + 1 16 θ 0 2 + 11 3072 θ 0 4 + … ) θ 0 = sin − 1 ( x L ) θ ( t ) = θ 0 cos ( 2 πt T ) h = L − √ L 2 − x 2 ∆ K + ∆U = 0 K = 1 2 mv 2 U = mgh

Discussion Experiment Overview: In this experiment, we were required to determine the relationship between the period of a pendulum and different parameters including the string length(s), the masses of bob 1 and 2, amplitude of oscillation, and the conservation of energy of the pendulum. The materials we worked with were two bobs, a string, a balance, a caliper, a meter stick and a photogate. We started by recording the colour of the bobs and measured the mass and diameter of each one. Oscillation Using the photogate, we measured the period of oscillation as the bob swings from a pivot point. We recorded a total of 10 oscillations with 5 different string lengths. We recorded the information on the Logger Pro Simple pendulum analysis. After using 5 different string lengths with one bob, we changed the bob and recorded the oscillation for one string length. Amplitude effect We selected a bob and put the length of the string at 37.5 cm for this experiment. We recorded the velocity at the equilibrium position in the analysis logger pro file. We measured a total of 6 oscillations and recorded it in the file. Analysis: The mass of a child or adult will make a difference in the periods on a swing. In this experiment, we measured the oscillations using the same mass. When on a swing, the mass of a child is lighter so the speed of which the swing moves will be affected changing the periods. This is the same with an adult, a heaver weight will cause more force on the swing. An Adult mass will result in more friction whereas the child’s mass will have less friction. Sources pf uncertainty: Some of the limitations could include not having multiple masses for bobs. Measuring different masses with varying legths could help us have a more accurate result. Improvements: Having a force sensor could help give us more accurate results as we can track the force of the mass against the string while its moving. This could help us determine how the mass effects the oscillation periods.