Question

. Suppose a new tire has a tread depth of 11.2 mm. As the tire begins to wear from use, the depth of each tread decreases. Legally, tires must have a minimum tread of 1.6 mm. However, most tire experts suggest changing the tires before the tread reaches 3.2 mm.

a. The tire treads were measured to have a depth of 7 mm using a ruler with a precision of 1 mm. Determine the amount of tread that has worn off, including the uncertainty.

b. You measured your tire treads to be 3.3 ± 0.2 mm. Is it time to change your tires? Explain.

Answer 1

a.
Initial tread depth = 11.2 mm
Measured tread depth = 7 mm
Uncertainty = ± 1 mm

Amount of tread worn off = Initial tread depth - Measured tread depth
= 11.2 mm - 7 mm
= 4.2 mm

Therefore, the amount of tread that has worn off, including the uncertainty, is 4.2 ± 1 mm.

b.
Measured tread depth = 3.3 ± 0.2 mm
Minimum tread depth recommended by tire experts = 3.2 mm

Since the measured tread depth of 3.3 mm is very close to the minimum recommended tread depth of 3.2 mm, it is best to change the tires soon to ensure safety and optimal performance. The uncertainty of ± 0.2 mm should also be taken into consideration as it could potentially mean that the actual tread depth is lower than 3.2 mm.