Answered: you are conducting a free-fall…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

you are conducting a free-fall experiment by dropping a ball multiple times from a height of y = 1.00 m and measuring the time of fall t. Your results for 4 trials are t = 0.459 s, 0.448 s, 0.452 s, and 0.453 s. Using this data, what is the average value of g?

Expert Solution

Step 1

Given:

The height form which the ball is dropped is y=1 m.
The time of ball in first trial is t₁=0.459 s.
The time of ball in second trial is t₂=0.448 s.
The time of ball in third trial is t₃=0.452 s.
The time of ball in fourth trial is t₄=0.453 s.
The acceleration due to gravity is g.

The expression to calculate gravitational acceleration is given by,

$\begin{array}{rcl} y & = & \frac{1}{2} g t^{2} \\ g & = & \frac{2 y}{t^{2}} \end{array}$

Substitute the values of t for the first trial in the above expression.

$\begin{array}{rcl} g_{1} & = & (\frac{2 \times 1 m}{{(0.459 s)}^{2}}) \\ g_{1} & = & 9.493 m / s^{2} \end{array}$

Substitute the values of t for the second trial in the above expression.

$\begin{array}{rcl} g_{2} & = & (\frac{2 \times 1 m}{{(0.448 s)}^{2}}) \\ g_{2} & = & 9.964 m / s^{2} \end{array}$

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