Work done by the frictional force is

In two separate collisions,the coefficients of restitution $e_1$ and $e_2$ are in the ratio $3:1$. In the first collision,the relative velocity of approach is twice the relative velocity of separation. Find the ratio between the relative velocity of approach and the relative velocity of separation in the second collision.

$A$ person trying to lose weight by burning fat lifts a mass of $10 \ kg$ up to a height of $1 \ m$, $1000$ times. Assume that the potential energy lost each time he lowers the mass is dissipated. How much fat will he use up considering the work done only when the weight is lifted up? Fat supplies $3.8 \times 10^7 \ J$ of energy per $kg$, which is converted to mechanical energy with a $20\%$ efficiency rate. Take $g = 9.8 \ m/s^2$.

$A$ spring-block system is resting on a frictionless floor as shown in the figure. The spring constant is $2.0 \,N \,m^{-1}$ and the mass of the block is $2.0 \,kg$. Ignore the mass of the spring. Initially, the spring is in an unstretched condition. Another block of mass $1.0 \,kg$ moving with a speed of $2.0 \,m \,s^{-1}$ collides elastically with the first block. The collision is such that the $2.0 \,kg$ block does not hit the wall. The distance, in metres, between the two blocks when the spring returns to its unstretched position for the first time after the collision is. . . .

$A$ body of mass $2.9 \, kg$ is suspended from a string of length $2.5 \, m$ and is at rest. $A$ bullet of mass $100 \, g$ strikes the block horizontally with velocity $150 \, m/s$ and sticks to it. What is the maximum angle made by the string with the vertical after the impact? (Given $g = 10 \, m/s^2$)

$A$ bullet of mass $25 \,g$ moving horizontally at a speed of $250 \,m/s$ is fired into a wooden block of mass $1 \,kg$ suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of mass of the block rises through a height of $20 \,cm$, find the speed of the bullet as it emerges from the block. (Take $g = 10 \,m/s^2$) (in $\,m/s$)