Lab Report #2 Determining g on an Incline - PCS120

Lab Report 2 Determining g on an Incline Jewel Benita Ungao Aashwin Mittal PCS120 Section 5 Jian Yuan Filip Bodera

I. Introduction The objective of this experiment is to examine an object's gravitational acceleration (g) and be able to identify the value of g in relation to various inclinations. Furthermore, it aims to establish a connection between different angles and the cart’s acceleration as it rolls down an incline. It also intends to justify the validity of this experiment that seeks to illustrate the value of g which is 9.80 m/s 2 by extrapolating data from a free falling object. II. Theory It is assumed that the cart will go along the tracks while accelerating until it hits a point and then changes its direction, reaching the maximum point on the incline and then follows the same procedure until it comes to rest which will leave the velocity at = 0 m/s. The acceleration of the cart when released from the point is called acceleration due to gravity (g). ∆? = 1 2 𝑎∆? 2 → ∆? = 1 2 𝑔?𝑖?θ · ∆? 2 ∆? Final velocity - initial velocity ∆? Final time - initial time θ Angular position The velocity time graph roughly looks like this and the slope of the gray line on the graph provides the acceleration due to gravity.

IV. Results and Calculations Runs Height of Incline (cm) Length of Incline (cm) θ Acceleration Average Acceleration ?/? 2 Trial 1 ?/? 2 Trial 2 ?/? 2 Trial 3 ?/? 2 1 17 cm 100 cm 0.17 ° 5.87 6.02 6.09 5.99 ± 0.091 2 25 cm 100 cm 0.25 ° 28 28 28.2 28.06 ± 0.244 3 13 cm 100 cm 0.13 ° 11.41 11.41 11.41 11.41 ± 0.0 4 20 cm 100 cm 0.20 ° 11.60 11.82 12.85 12.09 ± 0.544 Sample calculation (Run #1 Trial #1) To calculate : θ Sin = θ ?????𝑖?𝑒 ℎ????𝑒???𝑒 = ℎ𝑒𝑖𝑔ℎ? ?𝑒?𝑔?ℎ Sin = θ 17𝑐? 100 𝑐? = 0. 17° To calculate acceleration: 2 ∆? = 1 2 𝑔?𝑖?θ (∆?) ∆? = 1. 5 − 0. 25 = 1. 25 ∆? = 1. 08 − 0. 3 = 0. 78 0. 78 = 1 2 𝑔 0. 17 (1. 25) 2 = = 5.87 9.18 1.5625 Mean Value: µ = Σ? 𝑁 µ = 5.99 + 11.41 + 12.09 3 = 9. 83 ?/? 2 = 2.73 σ = (5.99 − 9.83) 2 +(11.41 − 9.83) 2 +(12.09 − 9.83) 2 3 ?/? 2 Error = % 𝐴𝑐??𝑎? ?𝑎??𝑒 − 𝑇ℎ𝑒??𝑒?𝑖𝑐𝑎? 𝑉𝑎??𝑒 𝐴𝑐??𝑎? 𝑉𝑎??𝑒 • 100 9.80 ?/? 2 − 9.83?/? 2 9.80?/? 2 · 100 = − 0. 3% | | = 0. 3%

Graphs (Position-Time & Velocity-Time graphs) Run 1 (Trials 1-3) Run 2 (Trials 1-3)

eliminated from the calculations. By implementing such modification, it suggests that the collected data (9.83m/s²) now conforms to the referenced gravitational force acting on free falling objects on an incline (9.80m/s²). Therefore, the extrapolated value does agree with the actual value. VI. References Randall D Knight. Chapter 2 in Physics for scientists and engineers: A strategic approach with modern physics. Pearson. Professor pre lecture notes. Chapter 2 ,page 14.