Question 1 Answer:
Fc = mv2/r Fc = mv2/r
Fc = 80(3 x 3)/10.2 Fc = 80(3 x 3)/12.7
Fc = 80(9)/10.2 Fc = 80(9)/12.7
Fc = 720/10.2 Fc = 720/12.7
Fc = 70.6 N Fc = 56.7 N
The unicycle with the shorter cranks would require a larger force to stop.
Question 2 Answer:
20" = 50.8 cm = .508 m v = d/t
C = (pi)d v = 20/14
C = (pi).254 v = 1.43 m/s
C = .798 m
20/.798 = 25.06
v = d/t
v = 25.06/14
v = 1.79 m/s
The pebble was travelling at 1.79 m/s around the tire.
Question 3 Answer:
Eg = Ek a = vf - vi/t
mgh = 1/2mv2 a = 6.3 - 0/1.2
gh = 1/2v2 a = 6.3/1.2
9.8(2) = 1/2v2 a = 5.25 m/s2
2(19.6) = v2
39.2 = v2 f = ma
6.3 m/s = v f = 74(5.25)
f = 388.5 N
Yes the rim will hold up.
Question 4 Answer:
mava + mbvb = mava' + mbvb'
70(6.94) + 30(6.94) = 70(v) + 30(0)
485.8 + 208.2 = 70v
694 = 70v
9.9 m/s = v
The unicyclists velocity was 9.9 m/s after hitting the beaver.
Question 5 Answer:
C = (pi)d
643.5/336 = 1.915
1.915 = (pi)d
.6096 m = d
60.96 cm = 24"
She was riding a 24" wheel.
Question 6 Answer:
24" = 60.96 cm 28" = 71.12 cm
Ac = v2/r Ac = v2/r
2 = v2/.3048 1.5 = v2/.3556 m
.6096 = v2 .5334 = v2
.7808 m/s = v .7303 m/s = v
John is going faster.
Question 7 Answer:
5" = 12.7 cm f = ma
t = rf 300 = 75(a)
38.1 = .127(f) 4 m/s2 = a
300 N = f
26" = 66.04 cm
Ac = v2/r
4 = v2/.3302
1.3208 = v2
1.15 m/s = v
The unicyclist will go 1.15 m/s.
