Answer to Question #183716 in Classical Mechanics for Robin

Question

1. two bodies have the masses m and M, respectively. They move from the beginning with the velocity v directed in the positive direction and v directed in the negative x direction.  the masses then collide in a completely inelastic shock and form a body with the mass M + m.  no rotation takes place after the impact.  how much of the kinetic energy is lost in the impact?
2. when observing an object through a magnifying glass, the observed object must be placed within the focal length of the lens.  we denote the focal length f, and the distance of the object from the lens b (f> b).  what is the ratio between the size of the virtual image and the size of the object?

Answer 1

1)

$\Delta T=\frac{mv^2}{2}+\frac{Mv^2}{2}-\frac{m+M}{2}(\frac{mv+Mv}{m+M})^2=\frac{mM}{2(m+M)}(v-v)=0.$

2)

$Г=\frac sb=\frac{bf}{(f-b)b}=\frac{f}{f-b}.$