Question

David’s son Harley wants to do a loop-the-loop on his new motorcycle. If he weighs 800 N, and his cycle weighs 2500 N, what minimum speed will he need so as not to fall on his head?

Answer 1

Hi buddy!

In this case it is a vertical loop! Keep in mind that cenripetal force along vertical loop is different from a horizontal one. In the case of horizontal loop there is only the angular acceleration acting, while in a vertical loop, the angular acc + acceleration due to gravity each time the motorcycle comes down the loop.

In simple words it is centripetal force or,

Fc = F_N + F_g

where F_c = centripetal force, F_N = normal force and Fg = gravitational force

Fg can be taken as mg.

In order to calculate the minimum speed in order to sustain a vertical motion , Fn or the normal force is taken as zero.

(mass and g value is const. only velocity can be changed to sustain rotation)

Thus

where r = radius of the loop

We need the value of radius and Fg = 3300N approx 336.5 kg