Bob is towing a trailer. One of the trailer\'s tires is bad. Bob does not have a
ID: 1476652 • Letter: B
Question
Bob is towing a trailer. One of the trailer's tires is bad. Bob does not have a replacement tire, but he has an old wheel of a different size that he uses to change out one of the trailer's wheels. One wheel has tires with a radius of 10.2 inches. The other wheel has tires with a radius of 12.7 inches. Bob drives down the road at a constant speed of 47.5 mph.
a) Determine the rotational rate of each wheel (in radians per second).
b) Determine how many times each wheel turns after Bob has driven a distance of 4.25 miles.
Explanation / Answer
here,
radius of the old wheel , r = 10.2 inch
r = 0.259 m
radius of the wheels , r' = 12.7 inch
r' = 0.323 m
speed of trailer , v = 47.5 mph
v = 21.23 m/s
a)
the rotational rate of old wheel , w = v/r
w = 21.23/0.259
w = 81.97 rad/s
the rotational speed of new wheels , w' = v/r'
w' = 21.23/0.323
w' = 65.77 ard/s
b)
distance travelled , d = 4.25 miles
d = 6839.71 m
number of rotation for old wheel , n = d/( 2*pi*r)
n = 6839.71/( 2*pi*0.259)
n = 4205.12 rotations
the number of rotations for new wheels , n' = d/( 2*pi*r')
n' = 6839.71/( 2*pi*0.323)
n = 3371.91 rotations