Chapter 6: Q. 110 (page 367)

A spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested? Express your answer in miles per hour. At how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour?

Short Answer

Expert verified

The road speed being tested is 37.13 miles per hour and the number of revolutions per minute should be 1034.26 to be set to test a road speed of 80 miles per hour.

Step by step solution

Given information

A spin balancer rotates the wheel of a car at 480 revolutions per minute and the diameter of the wheel is 26 inches.

Calculate the road speed.

As we know,

$Linear velocity (v) = r \times \frac{θ}{t} 1 revolution = 2 π radian per minute$

And,

$480 revolution = 480 \times 2 π = 960 radian per minute$

So that,

$v = 13 \times \frac{960 π radian}{1 minute} = 39207.0763 inch per minute$

1 milelocalid="1652163269849" $= 63360 inch$

1 hour $= 60 minute$

Therefore,

39207.0763 inch / \min = \frac{39207.0763}{63360} \times 60 mile / h = 37.13 mile / h

Thus, the road speed being tested is 37.13 miles per hour.

Calculate the revolutions per minute should the balancer be set to test a road speed of 80 miles per hour,

$Circumference = 2 πr = 26 π inches$

$\frac{80 miles}{1 hour} \times \frac{5280 ft}{1 mile} \times \frac{12 inch}{1 ft} \times \frac{1 rev}{26 π inch} \times \frac{1 hour}{60 minute} = 1034.26 rev . / minute$

The number of revolutions per minute should be 1034.26 to be set to test a road speed of 80 miles per hour.

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A spin balancer rotates the wheel of a car at 480 revolutions per minute. If the diameter of the wheel is 26 inches, what road speed is being tested? Express your answer in miles per hour. At how many revolutions per minute should the balancer be set to test a road speed of 80 miles per hour?

Short Answer

Step by step solution

Given information

Calculate the road speed.

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