Question

At takeoff a commercial jet has a 70.0 m/s speed. Its tires have a diameter of 0.400 m.

(a) At how many rpm are the tires rotating?
  rpm
(b) What is the centripetal acceleration at the edge of the tire?
  m/s²
(c) With what force must a determined 10^-15 kg bacterium cling to the rim?
N
(d) Take the ratio of this force to the bacterium's weight.
(force from part (c) / bacterium's weight)

(a) A 23.0 kg child is riding a playground merry-go-round that is rotating at 45.0 rpm. What centripetal force must she exert to stay on if she is 2.50 m from its center?
  N
(b) What centripetal force does she need to stay on an amusement park merry-go-round that rotates at 3.00 rpm if she is 5.00 m from its center?
  N
(c) Compare each force with her weight.
  (force from part (a) / weight)
  (force from part (b) / weight)

All of these answers wrong someone please help me.

Answer 1

(a)

(a)ω

v = speed = 70 m/s

r = Diameter of tire/2 = 0.400 m/2 = 0.200 m

ω = 70/0.200 = 350 rad/s

(a) ω = 350 rad/s *1rev/2π rads *60 s/min = 3343.949 rpm = 3344 rpm

(b) Centripetal acceleration = a = ω²r = (350 /s)²0.2 m = 24500 m/s²

(c) Force = mass * a = 1*10^-15kg * 24500 m/s² = 2.45 * 10^-11 N

(d) Ratio = 24500 / 9.8 = 2500

(a) The child move a distance of 2.5 m which is equal to circumference of the circle, as the merry-go-round rotates one time. So circumference = 2*π * 2.5 m = 15.7 m

The distance child moves in 45 rotations

D = 45 * π * 5.0 m = 225.0*π = 706.5 m

Velocity = D/ Time = 706.5 / 60 = 11.775 m/s

Centripetal force = m * v²/r = 23 * (11.775)²/2.5 = 1275.58 N

(b)

The child move a distance of 5.0 m which is equal to circumference of the circle, as the merry-go-round rotates one time. So circumference = 2*π * 5.0 m = 31.4 m

The distance child moves in 3 rotations

D = 3 * π * 10.0 m = 30.0*π = 94.2 m

Velocity = D/ Time = 94.2 / 60 = 1.57 m/s

Centripetal force = m * v²/r = 23 * (1.57)²/5.0 = 11.338 N

(c) part (a) Force = 1275.58 N

part (b) Force= 11.34 N

force(a)/weight = 1275.58/ (23* 9.8) = 5.65

force(b)/weight = 11.34 / (23* 9.8) = 0.05