Answer to Question #244110 in Physics for Markien

Question

III. EXERCISE Directions: Solve the problems and show the complete solution in each item.

1) A Ferris wheel is standing 50 stories high and can hold 800 passengers. It has a diameter of 200m and takes approximately 30mins to make a full circle.

a) Determine the vT or simply v of riders in m/s. ( vT = 2πr / T )

2) A bicycle wheel of R 1.3m undergoes 25 rotations in 60s.

a) Find total distance travelled (Number of rot * (2πr))

b) Find vT

c) Find a

Answer 1

1) a) The speed of riders in m/s is

$$v=\frac{\pi D}{T}=\frac{3.14·200}{30·60}=0.35\text{ m/s}.$$

2) a) The total distance is

$$D=n·2\pi r=\bigg(\frac{25}{60}\bigg)·2\pi·1.3=3.4\text{ m}.$$

b) The tangential velocity is

$$v=\omega r=(2\pi n)r=(2\pi·25/60)1.3=3.4\text{ m/s}.$$

c) The centripetal acceleration is

$$a=\frac{v^2}{r}=8.9\text{ m/s}^2.$$