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.


The velocity of the block is given as


Given


The spring with a spring constant of k, at a height of h forming at an angle of 37o


Formula Used


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



where


m is the mass of the object, v is the velocity, k is the spring constant and x is the elongation distance.


Explanation


To find the speed of the block moved from the resting position is given as





Due to 37o angle forming the height is written in terms of





Placing the height of the horizontal plane and block as




Hence, the velocity of the block is given as


1