Question

8) For the figures below, all surfaces are frictionless. All masses are identical. All masses start from rest. 5 m 2 m 10 m 1 m 5.7 5.32 B1 10.0& A 10 m 2 m 5 m 11.1 5.011 C 1 m a) Rank in order from greatest to least the final velocities of the blocks. Explain your ranking. Show work and calculations. b) Rank in order from greatest to least the time it takes each block to reach the bottom. Explain your ranking. Show work and calculations.

Answer 1

a)

Final velocity at the end of the incline is function of height only since,

$V = \sqrt{mgh}$

here h = 2m & 1m only.

So mass in B & D will have greater velocity than mass in A & C configuration.

(b)

If we resolve components of weight then (mgSinX) is the component along the inclined edge (X is the angle of inclination)

then acceleration along inclined edge (a) is given as a = F/m = (mgSinX)/m = gSinX ----------(1)

consider the equation s = ut+(1/2)at² here, s is hypotenuse of the incline and u is initial velocity.

time required to reach the bottom is    $t = \sqrt{\frac{2s}{a}} = \sqrt{\frac{2s}{gSinX}}$

Using above formula one sees that t are in the decreasing order are: A , D, C, B