Q49 of 101 Page 132

A small heavy block is attached to the lower end of a light rod of length l which can be rotated about its clamped upper end. What minimum horizontal velocity should the block be given so that it moves in a complete vertical circle?

Given


The length of the rod attaching the block is given as l.


Formula Used


Using the conservation of static and dynamic energy such as potential and kinetic energy, we have the conservation equation as



where


m is the mass of the object, v is the velocity, g is the acceleration due to gravity and h is the height at which the object is kept.


Explanation


Equating the conservation of energy, we get the minimum velocity of the block to complete a vertical circle, the length is double when forming circle




The minimum velocity of the block is


More from this chapter

All 101 →
47

A block of mass sliding on a smooth horizontal surface with a velocity meets a long horizontal spring fixed at one end and having spring constant k as shown in figure (8-E10). Find the maximum compression of the spring. Will the velocity of the block be the same as when it comes back to the original position shown?


 48

A small block of mass 100 g is pressed against a horizontal spring fixed at one end to compress the spring through 5.0 cm (figure 8-E11). The spring constant is 100 N/m. When released, the block moves horizontally till it leaves the spring. Where will it hit the ground 2 m below the spring?


 50

Figure (8-E12) shows two blocks A and B, each having a mass of 320 g connected by a light string passing over a smooth light pulley. The horizontal surface on which the block A can slide is smooth. The block A is attached to a spring of spring constant 40 N/m whose other end is fixed to a support 40 cm above the horizontal surface. Initially, the spring is vertical and unstretched when the system is released to move. Find the velocity of the block A at the instant it breaks off the surface below it. Take g = 10 m/s2.


 51

One end of a spring of natural length h and spring constant k is fixed at the ground and the other is fitted with a smooth ring of mass m which is allowed to slide on a horizontal rod fixed at a height h (figure 8-E13). Initially, the spring makes an angle of 37o with the vertical when the system is released from rest. Find the speed of the ring when the spring becomes vertical.