(13%) Problem 4: A bicyclist notes that the pedal sprocket has a radius of 7.-11
ID: 2268899 • Letter: #
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(13%) Problem 4: A bicyclist notes that the pedal sprocket has a radius of 7.-11.5 cm while the wheel sprocket has a radius of rw-5.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R 67 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every 19 s. when pedaling, the wheel sprocket and the wheel move at the same angular speed. tus p 11.5 cm w 5.5 cm R=67 cm Otheexpertta.c tus 17% Part (a) The pedal sprocket and the wheel sprocket have the same 17% Part(b) Calculate the angular speed of the pedal sprocket aap, in radians per second. ? 17% Part (c) Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second. 411% Part(d) 17% Part (c) Calculate the liner speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground. 17% Part (f) If the cyclist wanted to travel at a speed of v2 = 45 m/s, how much time, in seconds, should elapse as the pedal makes one mpleted ompleted complete revolution? Deductions 1009 sinO cosO tanO ? (..). 7 8 9|HOME cotan0 asinO acos0 atan0 acotan0 sinh0 coshO tanh0 cotanh00 Attempts remaining A 45 6 12 3 I give up!Explanation / Answer
Given,
rp = 11.5 cm ; rw = 5.5cm ; R = 67 cm ; t = 1.9 s
a)Tangential speed at outer edges
b)wp = 2pi/T = 2 x 3.14/1.9 = 3.31 rad/s
wp = 3.31 rad/s
c)vp = rp w = 0.115 x 3.31 = 0.381 m/s
vp = 0.381m/s
d)Ww = 0.67/0.055 = 12.18 rad/s
w = 12.18 rad/s
e)v = 0.67x12.18 = 8.161 m/s
v = 8.161 m/s
f)t = 2 pi r/v
t = 2 x 3.14 x 0.115/4.5 = 0.16 s
Hence, t = 0.16 s
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