Answer:
Explanation:
Potential energy lost by mass = mgh 
= 10 x 9.8 x 2 = 196 J 
a ) If v be velocity of mass at the bottom , its kinetic energy will be stored in spring as elastic energy 
= 1/2 m v² = 1/2 k x² , k is spring constant , x is compression , m is mass falling down 
.5 x 10 v² = .5 x 500 x .75²
v = 5.3 m /s 
b ) kinetic energy of mass at the bottom 
= /2 m v²
= .5 x 10 x 5.3²
= 140.45 J 
energy lost by mass while coming down 
=potential energy at the top - kinetic energy at bottom 
=  196 - 140.45
= 55.55 J . 
This is equal to negative work done by friction 
work done by friction = - 55.55 J
c ) Since there will be no loss of energy in compression and extension of spring so , no loss of kinetic energy will take place of mass . So it wil have same velocity that is 5.3 m /s while on its return journey. 
d ) kinetic energy at the bottom = 140.45 
loss of energy by friction again 
= 140.45  - 55.55 
= 84.9 J 
If h be the height attained 
 mgh = 84.9
10 x 9.8 x h = 84.9 
 h = .866 m 
( We have assumed that loss of energy in return journey will be same due to friction . )