Question

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.

Answer 1

speed v =
`√(gd)`

Step-by-step 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 =
`√(gd)`