Question 6.Q.1: The reaction force Find the reaction force N as a function o...

Once the motion is determined (for example by equation (6.17)), the unknown constraint forces may be found by using the Second Law in reverse. In the present case, consider the component of the Second Law F = ma in the direction \overrightarrow{P O}. This gives

v^{2}=u^{2}-2 g b(1-\cos \theta)                      (6.17)

N-m g \cos \theta=m v^{2} / b,

where we have made use of the formula (2.17) for the acceleration of a particle in general circular motion. On using the formula for v² from equation (6.17), we obtain

a =-\left(\frac{v^{2}}{b}\right) \hat{ r }+\dot{v} \widehat{ \theta }                                (2.17)

N=\frac{m u^{2}}{b}+m g(3 \cos \theta-2)                        (6.18)

This gives the value of N as a function of θ while P remains in contact with the sphere.