To show that a ∝ F

Apparatus

Air-track with one vehicle, pulley and blower, two photogates, two retort stands, dual timer, metre-stick, black card, set of slotted weights (1 N total).

Procedure

• Set up the apparatus as in the diagram. Make sure the card cuts both light beams as it passes along the track.

• Allow the trolley to roll down the runway.

• Level the air track.

• Set the weights F at 1 N. With the card at one end of the track start the blower and release the card from rest.

• Note the times t₁ and t₂.

• Remove one 0.1 N disc from the slotted weight, store this on the vehicle, and repeat.

• Continue for values of F from 1.0 N to 0.1 N.

• Use a metre-stick to measure the length of the card l and the separation of the photogate beams s.

• Record results as shown.

• Draw a graph of a/m s⁻² against F/N.

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To show that a ∝ F

Results

$l$ = .......... $m$.

$s$ = .......... $m$.

Initial velocity $u = \frac{l}{t_1}$

Final velocity $v = \frac{l}{t_2}$

Acceleration $a = \frac{v^2 - u^2}{2s}$

F/N	$t_1$/N	$t_2$/N	u/m s$^{-1}$	v/m s$^{-1}$	a/m s$^{-2}$
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1

Conclusion

A straight line through the origin shows that, for a constant mass, the acceleration is proportional to the applied force.