Question

Calculate your apparent weight at the top and bottom of a Ferris wheel, given that the radius of the wheel is 7.2 m, it completes one revolution every 28 s, and your mass is 55 kg

Answer 1

559.5 N at the bottom and 519.6 N at the top of the wheel

Step-by-step explanation:

If it completes 1 revolution (or 2π rad) per 28s then its angular speed is

`\omega = 2\pi/28 = 0.224 rad/s`

The centripetal acceleration would be:

`a_c = \omega^2 R = 0.224^2*7.2 = 0.363 m/s^2`

Let gravitational acceleration g = 9.81 m/s2.

At the bottom of the wheel the net acceleration would be g plus the centripetal acceleration:

`a_b = a_c + g = 9.81 + 0.363 = 10.17 m/s^2`

So the weight at the bottom of the wheel would be

`W_b = a_b*m = 10.17*55 = 559.5 N`

Similarly at the top of the wheel the net acceleration is g subtracted by the centripetal acceleration:

`a_t = g - _a_c = 9.81 - 0363 = 9.45 m/s^2`

And the weight at the top is

`W_t = a_t*m = 9.45*55 = 519.6 N`