Q45 of 101 Page 132

Consider the situation shown in figure
(8-E8). Initially the spring is upstretched when the system is released from rest. Assuming no friction in the pulley, find the maximum elongation of the spring.


The maximum elongation of the spring is


Given


As shown in the diagram, the spring constant is given as “k”, and the mass of the block is given as “m”.


Formula Used


Using the conversation of mass, we equate the energies of spring compression and potential energy of the mass of the block, the formula of the energy stored in spring compression is



And the energy stored in the block is formulated as



where


The value of spring constant is denoted as “k”, the compression distance is “x”, the mass of the block is given as “m”, the gravity of the block is “g” and the height at which the block is kept is h.


Explanation


The h, in the potential energy of the block is given as x, equating the potential energy with the spring energy is




Now we can say that the maximum elongation of the spring is


More from this chapter

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43

Figure (8E7) shows a spring fixed at the bottom end of an incline of inclination 37°. A small block of mass 2 kg starts slipping down the incline from a point 4.8 m away from the spring. The block compresses the spring by 20 cm, stops momentarily and then rebounds through a distance of 1 m up the incline. Find (a) the friction coefficient between the plane and the block and (b) the spring constant of the spring. Take g = 10 m/s2.


 44

A block of mass m moving at a speed u compresses a spring through a distance x before its speed is halved. Find the spring constant of the spring.

 46

A block of mass m is attached to two upstretched springs of spring constants k1 and k2 as shown in figure (8-E9). The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position shown.


 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?