- #1

chickyroger

- 2

- 0

## Homework Statement

Two blocks of equal mass are connected by a rope of negligible mass that is passed over a frictionless pully. The angle made by the horizontal plane and the ramp is 30 degrees.

a) If neither block moves, what is the required coefficient of static friction to keep the upper block from moving?

b) If the ramp is replaced by a frictionless ramp, how fast will the blocks be traveling when the lower mass descends by 0.5 meters?

## Homework Equations

F = ma

KE

_{initial}+ PE

_{initial}= KE

_{final}+ PE

_{final}

## The Attempt at a Solution

a) For the block hanging on the pulley:

F

_{net}= Mg - F

_{T}

ma = Mg - F

_{T}

For the block on the ramp:

ma = F

_{T}- Mgsin30 - [itex]\mu_{k}[/itex]gcos30

Then I set the two equations equal to each other:

Mg - F

_{T}= F

_{T}- Mgsin30 - [itex]\mu_{k}[/itex]gcos30

Mg = -Mg(sin30 + [itex]\mu_{k}[/itex]cos30)

-1 = sin30 + [itex]\mu_{k}[/itex]cos30

[-1-sin30]/cos30 = [itex]\mu_{k}[/itex] = -[itex]\sqrt{3}[/itex]

I got a negative number for static fricton?

b) I have no idea how to do this problem ): Do I use the conservation of energy formula to find velocity? so it'd be something like:

0 + Mg(0.50) = 1/2Mv

^{2}+ 0

v = 3.13 m/s

Someone please check if I am right!