Acceleration due to gravity.

(i) In general, an object moving with an initial velocity and a constant acceleration

s = ut + 1/2 at2

(ii) For an object initially at rest falling in a gravitational field

h = 1/2 gt2

I intend to investigate acceleration due to gravity on earth by free fall using the light gate experiment and with the above equation try to come up with a value for it.

Aim:

To determine the acceleration due to gravity by free fall.

Apparatus:

Electromagnet (Solenoid)

Steel ball bearing

Electronic timer

Trapdoor

Retort Stand

Diagram:

Method:

. Clamp the solenoid and trapdoor in the same vertical line.

2. Connect these two components to the centisecond timer as shown in the diagram above. Connect the timer to the mains and close the solenoid switch.

3. The solenoid should now be energised and will support the ball bearing. If this is not the case, check the electrical contacts to trapdoor until both circuits are established.

4. Open the switch to the solenoid, the ball bearing should now fall and the clock will start. When the trapdoor opens the clock will stop, showing the time of fall. The ball should hit the trapdoor as far as possible from the hinge, in order that the door opens with the least delay.

5. Remake the circuits and reset the centisecond timer.

6. Measure the distance h, as shown in the diagram. From the bottom of the ball to the top of the trapdoor.

7. Determine the time of fall, t, at least three times for this height and calculate its average value.

8. Repeat the measurement for at least six different heights over a range of about one metre.

Results:

h (m)

Time of fall t (s)

Time squared t2 (s2)

Readings

Average

0.4

0.3

0.3

0.31

0.30

0.09

0.5

0.33

0.33

0.35

0.34

0.11

0.6

0.37

0.37

0.37

0.37

0.14

0.7

0.39

0.39

0.39

0.39

0.15

0.8

0.42

0.43

0.42

0.42

0.18

0.9

0.46

0.45

0.45

0.45

0.21

.0

0.47

0.48

0.48

0.48

0.23

.1

0.49

0.49

0.49

0.49

0.24

Theory:

Object falling freely with uniform acceleration travels a distance of

h = ut + 1/2 at2

Where u = initial velocity

a = acceleration

t = time of fall

Since the object is falling the acceleration is replaced by gravity, g.

The ball is dropped from height so the initial velocity is zero. This will change the equation to

h = 1/2 gt2

Making gravity the subject formula

g = 2( h/t2)

Calculation:

From the graph behind

Gradient = t2/h

0.22 - 0.15

- 0.675

=

=

0.07

0.325

= 0.2154

If t2/h = 0.2154 then h/t2 = 1/0.2154

Substituting in g = 2 (h/t2)

g = 2 x 1/0.2154

= 9.29 ms-2

Evaluation:

The results for gravity from the experiment 0.51 ms-2 behind the actual value, which is 9.8ms-2.

The percentage accuracy = 9.29 /9.8 x 100

= 95% accurate

The accuracy of the experiment have been reduced due to some errors in the experiment. This includes air resistance. This causes the ball bearing to fall slower. But this can be neglected as it has a small error on the whole experiment. I think the main error came from the meter rule. As I used a meter rule of 1 meter, I found it difficult to measure heights above 1 meter. So I had to do some rough estimates when measuring the heights. The experiment itself was conducted below eye level. This I think might have paved a way for error of parallax when reading the meter rule.

Conclusion:

As my results has a high percentage accuracy, I am sure that if I were to rectify the recognised causes of errors, I would easily be able to get an answer very close to 9.8m/s2. The errors had an effect on the final outcome of my calculation.