A cycle mechanic checks the speed display on an electric bicycle. Fig. 1 shows the wheel diameter and the distance travelled in one complete rotation. The v...
Question 1 Report
A cycle mechanic checks the speed display on an electric bicycle. Fig. 1 shows the wheel diameter and the distance travelled in one complete rotation. The valve cap is removed before the diameter is measured. During a test on level ground, the wheel makes 40 complete rotations in 10 s. Assume that the tyre does not slip on the road.
(a) State the equation used to calculate the circumference of a circle from its diameter. [1]
(b) Calculate the circumference of the wheel. [2]
(c) Calculate the distance travelled by the bicycle in 40 rotations. [2]
(d) Calculate the speed of the bicycle in m/s. [2]
(e) Convert this speed into km/h. [2]
(f) Explain why measuring the diameter in metres is useful in this calculation. [2]
(g) State the SI unit of speed. [1]
Answer Details
(a) \(\text{circumference}=\pi\times\text{diameter}\). [1]
(b)
\[C=\pi\times0.70\text{ m}=2.20\text{ m}\]
[2]
(c) With no slipping, each complete rotation moves the bicycle by one circumference:
\[40\times2.20\text{ m}=88.0\text{ m}\]
[2]
(d)
\[v=\frac{88.0\text{ m}}{10\text{ s}}=8.8\text{ m/s}\]
[2]
(e)
\[8.8\times3.6=31.7\text{ km/h}\approx32\text{ km/h}\]
[2]
(f) Measuring diameter in metres gives circumference and distance in metres. Dividing that distance by time in seconds therefore gives speed directly in \(\text{m/s}\). [2]
(g) The SI unit of speed is \(\text{m/s}\). [1]
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