PROBLEMS
42
At what value of ex (the angle between the thread and the vertical, Fig. 41) will the thread be broken if it can withstand twice the weight of the ball? What will the trajectory of the ball be like after ,,,,...----....the thread is broken? ./ '" 129. A man swings a stone of mass / I \ 1 kg uniformly round in a vertical I \ \\ plane (Fig. 42). The stone is atta,II I \ I ched to a thread that can withstand \ I a tension of 4 kgf. The axis of rota\ / tion is at a distance of h == 4 ill from I / the ground. The radius of the circle described by the stone is l = 1 m. With what angular velocity must the stone be swung round to break Fig. 42 the thread? At what distance S from the man will the stone fall? 130. A small body of mass m slides without friction from the top of a hemisphere of radius R (Fig. 43). ./
Fig. 43
Fig. 44
At what h.eight will the body be detached from the surface of the hemisphere? 131. A ball slides without friction down an inclined chute from a height h and then moves in a loop of radius R (Fig. 44). What is the pressure exerted by the ball on the chute at a certain point B if the radius drawn from the centre of the loop to the point B makes an angle ex with the vertical? The mass of the ball is m and the height h == 5/2R. Consider the size of the ball as negligible.