Disk brakes, such as those in your car, operate by using pressurized oil to push

Question

Disk brakes, such as those in your car, operate by using pressurized oil to push outward on a piston. The piston, in turn, presses brake pads against a spinning rotor or wheel, as seen in the figute . Consider a 15kg industrial grinding wheel, 26cm in diameter, spinning at 950rpm . The brake pads are actuated by 2.1cm--diameter pistons, and they contact the wheel an average distance 10cm from the axis.

If the coefficient of kinetic friction between the brake pad and the wheel is 0.61, what oil pressure is needed to stop the wheel in 4.8s ?

Explanation / Answer

the distance travelled by the wheel in t = 4.8 s is
S = ut + (1/2)at2
u = r1 * w where r = ((26 - 10)/2) cm = 8 cm = 8 *10-2 m and w = 950 rpm = 950 * (2/60)radian/s
= 950 * (2 * 3.14/60) radian/s = 99.4 radian/s
a = (u2/r)
we know that
v2 - u2 = 2kaS
or v = [u2 + 2kaS]1/2
k = 0.61
the acceleration of the wheel is
a = (v/t)
or a = ([u2 +2kaS]1/2/t)
the oil pressure needed is
P = (F/A) = (m * a/ * r2)

put
m = 15 kg and r = 26 cm = 26 * 10-2 m

to get the answer

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