Question

In an experiment to verify Newton’s second law, a toy train was pulled along a straight wooden track. The train started at rest, and its final speed after travelling 1.0m was measured using a speed gun. The results are summarised in the table below.

 

Force / N Final speed / m/s

0.5 0.60

1.0 0.84

2.0 1.34

4.0 1.87

6.0 2.19

8.0 2.59

10.0 2.85

 

a.    Calculate the acceleration of the cart for each of the applied pulling forces.

b.    Draw a fully labelled scatter plot of force (y-axis) vs acceleration (x-axis).

c.    Do the results verify Newton’s second law. Briefly justify your answer?

d. Given that the mass of the train was measured using a top pan balance to be 0.40 kg, can you say anything else about the results?

Answer 1

Explanations & Calculations

1)

• Using the equation $\small v^2 =u^2 +2as \to a= \large \frac{v^2}{2s}$ for the motion of the cart, its acceleration can be calculated.

$\qquad\qquad \begin{aligned} \small a_1&=\small \frac{(0.6m)^2}{2\times1m}=0.180ms^{-2}\\ \small a_2&= \small \frac{0.84^2}{2}=0.353ms^{-2}\\ \small a_3&=\small \frac{1.34^2}{2}=0.898ms^{-2}\\ \small a_4&=\small \frac{1.87^2}{2}=1.748ms^{-2}\\ \small a_5&=\small \frac{2.19^2}{2}=2.398ms^{-2}\\ \small a_6&=\small \frac{2.59^2}{2}=3.354ms^{-2}\\ \small a_7&=\small \frac{2.85^2}{2}=4.061ms^{-2} \end{aligned}$

2)

• Data table & the corresponding graph

3)

• If we apply Newton's second law to the cart during its motion we get

$\qquad\qquad \begin{aligned} \small F-f&=\small ma\\ \small F&=\small ma+f \end{aligned}$

• It is of the shape $y=mx+c$.
• What we have received from the results is of this shape. (That f can be any uncertainty that may apply to the motion since the wooden track has friction )
• Therefore, we can partially conclude that the law is verified just because the shapes are tallied.

4)

• The gradient of the graph should give the magnitude of the mass in motion.
• Since the measured value of the cart is very much less than the gradient value, we can think the overall results are correspondent to the entire system in which may include the mass of the pulling means: ropes, etc or the test results are erroneous.