362 APPLIED MECHANICS 
4. A bicycle and rider, weighing together 180 lbs., are travelling at the rate 
of 10 miles per hour on the level. Supposing a brake is applied to the top of the 
front wheel, which is 30 inches in diameter, and this is the only resistance nevine 
how far will the bicycle travel before stopping if the pressure of the brake 
- 20 Ibs., and the ccefficient of friction is 0°5? [Inst.C.E.] 
5. Continuous brakes are now capable of reducing the speed of a train 
3% miles an hour every second, and take 2 seconds to be applied ; show in a 
tabular form the length of an emergency stop at speeds of 3%, 74, 15, 30, 45, 60 
miles per hour. Compare the retardation with gravity, and express the resisting 
force in lbs. per ton. [UL 
6. If the force available on the block of the brake on a wheel of a railway 
vehicle is 90 per cent. of the weight on the wheel, and if the coefficients of sliding 
friction between the block and the wheel and between the wheel and the rail are, 
at 60 miles per hour, 0°06 and 0°04 respectively, what is the maximum resistance to 
the motion of the wheel, in lbs. per ton, when the brake is applied, (a) when the 
wheel does not skid, () when the wheel skids, at the above speed ? 
7. To determine the brake horse-power of a small de Laval steam turbine a 
Prony brake was used. The brake was placed ona pulley on the second-motion 
shaft, whose speed was 2992 revolutions per minute. The brake load at 18 inches 
from the axis was 5 lbs. Calculate the brake horse-power. 
8. The internal diameter of a fly-wheel rim, which is of channel section, is 
5 feet. Find the minimum speed, in revolutions per minute, at which the wheel 
will hold, without spilling, a layer of water 1 inch deep. ; 
9. The brake horse-power of a gas-engine is to be measured with a rope brake 
on the fly-wheel. The diameter of the wheel is 5 feet, and the diameter of the 
rope is } inch. At a speed of 183 revolutions per minute the hanging weight 
is 674 he and the spring balance indicates 4} lbs. What is the brake horse- 
power 5 
10. In an epicyclic-train dynamometer of the form shown in Fig. 546, 
p. 356, the wheels on the axle CD run at 100 revolutions per minute. The weight 
W on the lever is 60 lbs., and its distance from the axis of the axle is 24 inches. 
Calculate the horse-power transmitted through the dynamometer, 
11. Fig. 551 shows a Froude and Thornycroft dynamometer for measurin 
the difference between the tensions on the tight and slack sides of a belt which 
is transmitting power from 
a poy A = a pulley B. 
The T shaped lever has its 
fulcrum at D, and carries xo™ 
pulleys E and F. The 
iameters of the pulleys 
are such that the straight 
parts of the belt may be A 
taken as horizontal. Ne- 
glecting the work lost in 
friction in the instrument, 
show that the horse-power wen 
transmitted is given by the formula, HP= 
sagas where d@ is the diameter 
of the pulley A, and N its speed in revolutions per minute, dimensions being in 
feet, and W in lbs. F 
12. The horse-power of a marine steam turbine was found by observing that 
the angle of twist of a 20-feet length of the propeller shaft at 480 revolutions per 
minute was 1°75 degrees, The shaft, which was solid, had a diameter of 7 inches, 
and it was known that the modulus of rigidity of the material of the shaft was 
12,000,000 Ibs. per square inch. Neglecting the effect of the end thrust, calculate 
the horse-power. 
