Physics

Problem

The table shows measurements taken for a toy train that travels at various constant speeds around a circular track. Speed

v

(m/s): 2.0 3.0 4.0 Centripetal acceleration

a_c

(m/s

^{2}

): 0.50 1.1 2.0 If a graph of

a_c

(vertical axis) versus

v^{2}

(horizontal axis) is drawn, what is the best estimate of the radius of the track? a)

12\text{ m}

4.0\text{ m}

8.0\text{ m}

6.0\text{ m}

Intuitive explanation

Circular motion ties speed and centripetal acceleration together through the relationship $a_c = \frac{v^2}{r}$ . When you plot $a_c$ against $v^2$ , you get a straight line whose slope is $\frac{1}{r}$ —so finding the radius is just a matter of calculating that slope from your data points and taking its reciprocal.

Intuitive explanation

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