Find the speed of the driven wheels in rpm

[tony_engin]

A car's typre has diameter 570mm, and the height of the centre of the axle
above the road is 260mm for the front wheels, and 270mm for the rear wheels.
Find the speed of the driven wheels in rpm when traveling at 60km/h.
The answer is 61.539rpm.

I can't get this answer...
can anyone help?

 

[HallsofIvy]

If the tyre has diameter 570 mm then it has diameter 570(3.14)= 1790 mm= 1.79 meters. That means that, assuming no slippage, every time the tire rotates once, the car moves forward 1.79 meters. 60 km/hr is 1 km/min= 1000 m/min. Okay, how many times does the tire have to rotate to move the car forward 1000 meters?

(The height of the axle is irrelevant to this problem.)

 

[tony_engin]

HallsofIvy,
yes..I tried this method as well..
It needs to rotate 1000/1.79 = 558.66 times per minute..
that means the required angular speed should be 558.66 rpm...
but this is different from the model answer...
how come?

 

[Astronuc]

I think the answer given, 61.539 rpm, is off by a factor 10.

If the axle is only 260 mm from the ground, then a 570 mm diameter tire is running low on air and does not have a true circular shape. The contact surface with the ground is flat and the effective diameter is less than the tire diameter. [That's why one gets better mileage with fully inflated or slightly over-inflated tires - but it's best not to over-inflate for safety reasons].

If the one uses the effective diameter of the wheel, the front wheel rotational speed is 1000 m/(pi*0.52) = 612.1 rpm and the rear wheel rotational speed is 1000 m/(pi*0.54) = 589.5 rpm. To obtain 615.4, the effective diameter would have to be 0.51724 m.

To get 61.4 rpm, the tire diameter would have to be 5.1724 m to cover 1000 m in one minute.