1. (7 points, suggested time 13 minutes)
Two blocks, with masses m and 3m, are attached to the ends of a string with negligible mass that passes over a
pulley, as shown above. The pulley has negligible mass and friction and is attached to the ceiling by a bracket.
The blocks are simultaneously released from rest.
(a) Derive an equation for the speed v of the block of mass 3m after it falls a distance d in terms of m, d, and
physical constants, as appropriate.

speed v =  

Explanation:

given data

mass 1 = m

mass 2 = 3m

solution

As per image attach we will apply here work energy theorem that is

Δ K.E = W( all )    ......................1

and K.E = 0.5 × m × v²    .............2

W  = mass × g ×  distance      .............3

here distance is d

put here value in equation 1

0.5 × m × v² + 0.5 × 3m × v²  = 3m × g × d - ( m × g × d )     ................4

solve it we get

2 × v² = 2 ×g ×d

v =  

force required to detach it is given by

charges are taken to be fundamental charge

now we have

so above is the minimum distance at which it will detach