La b 2

Definitions

Acceleration due to gravity: Acceleration with which any body falls, when it is falling freely with no air resistance or any other forces acting on it other than gravitational force, close to the surface of earth, is called acceleration due to gravity. It is denoted by' g ' and has the value of approximately 9.81 m/s2.

NOTE: For the case of our experiment, we will neglect air resistance, even though it is present, as it is negligibly small.

Free fall: Any body falling under this acceleration due to gravity, and with no other forces acting on it, is said to be in free fall motion.

Apparatus setup and concept

Key Idea: Drop bodies from rest through height h under free fall motion and record total time t of fall.

From Newton’s equation of motion for a body:

y− y0 = v0 t+ 1

2 a t

2 (1)

wherey is final position,y0 is initial position, v0 is initial velocity and a is constant acceleration.

In this case: y− y0 =−h , as final height is lower than initial, v0 = 0 , as body drops from rest and a =−g , acting downwards.

Final equation from (1), using these: h = 1

2 g t

2 (2)

Outline of procedure

Drop objects from different initial heights, recording all h values.

Record the total time of fallt for all these differenth . Compute average⟨t ⟩ for small and big balls. Using these data, create h vs.⟨t ⟩2 plots.

Then comparing Eqn. (2) with straight line equation

y = mx + b (3) with the correspondencey→h , x→ t2 , we determine acceleration due to gravity g from the slopes of the plots and take average of these values.

h

t 2

slope→g

Properties of acceleration due to gravity

Its magnitude does not depend on mass, shape, size and material of the object.

When close enough to the surface of the earth, its magnitude does not depend on the height from which the body is dropped.

Resulting Observation from these properties: In the absence of air resistance or any other forces, other than the gravitational force, all bodies dropped from the same height (which is much smaller compared to the radius of the earth) will reach the ground at the same time. We can recast equation(2) to clearly see that time of fall is

independent of mass and size of free-falling object: t = √ 2hg (4)

End of Theory

Provided data for Exp 2 and instructions for data analysis and lab report

1. Provided data for Exp 2 are given in Tables 1 & 2 (attached below).

2. Instruction for data analysis

(a) Calculate t(average) (s) and t2 (average) (s2) and record your calculated data in Tables 1& 2

respectively.

(b) Copy the data of t2(average) (s2) and h (m) from Table 1 (for big ball), and paste them in the

columns A and B in an Excel file.

(c) Plot the data h vs t2(average) and fit the data with a linear function y = mx + b where m is the

slope, b is the intercept. Record the slope in Table 1.

You can search on google to find out how to do plot and fit with Excel.

(d) Calculate (exp.)g and record it in Table 1

(e) Calculate % error between (exp.)g and ( .)acceptg . Record the % error in Table 1.

(f) Repeat steps (b) to (e) for small ball (the data are in Table 2).

Record in Table 2 the fitting slope as well as all of your calculated data for small ball.

3. Instructions for lab report

(a) Two figures of plotting and fitting for big and small balls must be included in your Exp 2 report.

(b) Tables 1 & 2 with all the analyzed data must be included in your Exp 2 lab report.

(c) Answers to the 4 questions at the end of Exp 2 lab manual must be included in your Exp 2 report.

(d) The required other contents and format for your lab report can be found in the syllabus.

Table 1 Data from Measurement #1: Free fall time of big ball ( 1m ) with heights:

1 2 3 4 5, , , ,h h h h h

h (m) Fall time t (s) of big ball ( 1m ) t(average)

(s)

t2 (average)

(s2)

Fitting

slope

(exp.)g ( .)acceptg

% error Trail 1 Trial 2 Trial 3

1.655 0.580 0.579 0.572 9.8

m/s2

1.455 0.543 0.543 0.536

1.255 0.509 0.507 0.493

1.055 0.462 0.455 0.445

0.855 0.410 0.410 0.415

Table 2 Data from Measurement #2: Free fall time of small ball ( 2m ) with heights:

1 2 3 4 5, , , ,h h h h h

h (m) Fall time t (s) of small ball ( 2m ) t(average)

(s)

t2 (average)

(s2)

Fitting

slope

(exp.)g ( .)acceptg

% error Trail 1 Trial 2 Trial 3

1.655 0.581 0.580 0.581 9.8

m/s2

1.455 0.542 0.542 0.546

1.255 0.502 0.506 0.499

1.055 0.465 0.452 0.458

0.855 0.408 0.409 0.407