# Blocks on Inclined Ramp Connected by Pulley

• chickyroger
In summary: Then the KE = PE equation becomes:KEfinal = PEinitial + (0.5 m)(PEinitial + PEfinal) = (0.5 m)(0 + (PEinitial + PEfinal)) = (0.5 m)(0.5 + PEfinal) KEfinal = 0.5 m(1.5 + PEfinal)
chickyroger

## 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
KEinitial + PEinitial = KEfinal + PEfinal

## The Attempt at a Solution

a) For the block hanging on the pulley:
Fnet = Mg - FT
ma = Mg - FT

For the block on the ramp:
ma = FT - Mgsin30 - $\mu_{k}$gcos30

Then I set the two equations equal to each other:
Mg - FT = FT - Mgsin30 - $\mu_{k}$gcos30
Mg = -Mg(sin30 + $\mu_{k}$cos30)
-1 = sin30 + $\mu_{k}$cos30
[-1-sin30]/cos30 = $\mu_{k}$ = -$\sqrt{3}$

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) = 1/2Mv2 + 0
v = 3.13 m/s

Someone please check if I am right!

I think its better to work without the energy way, let's use only the forces.

If we make the x' axe as the direction of the ramp and the y' axe perpendicular to it, wee see that the forces in the x' axes are:
$P$
$Psen30º$
and Friction force $Fa = N.u = P.cos30º.u$

Equaling:

$1,5P = P.cos30º.u -> u = \sqrt{3}$

Without the friction force the forces in the x' axe are $1,5P = 2ma -> a=\sqrt{30}/2$

$V² = Vo² + 2a\Delta S -> V = \sqrt{2a\Delta S} = \sqrt[4]{7,5}$

For part a

1. When the system is in equilibrium, ma = ?
2. In what direction does FT act on the mass on the incline? In what direction does mgsin30 act on that mass?

For part b

Yes you can use conservation of energy, but you need to determine the initial and final PE and KE of both blocks together, Each has initial speed 0 and final speed V. For PE of each, initial and final, you need to define a reference plane. Assume, at the start, the inclined block is 0.5 m up the slope from the bottom of the incline, and the hanging block is at the bottom of the incline. For the final position, the inclined block will be at the bottom of the incline, and the hanging block will be 0.5 m down from the bottom of the incline.

## 1. How does a pulley system affect the motion of blocks on an inclined ramp?

A pulley system can reduce the amount of force needed to move the blocks on an inclined ramp. By using a pulley, the force required to move the blocks is distributed between the two sides of the ramp, making it easier to lift the blocks.

## 2. What is the purpose of connecting the blocks with a pulley?

The purpose of using a pulley to connect the blocks is to change the direction of the force applied to the blocks. This allows for a more efficient transfer of energy and can make it easier to move the blocks up the inclined ramp.

## 3. How does the angle of the inclined ramp affect the motion of the blocks?

The angle of the ramp affects the motion of the blocks by changing the amount of force needed to move them. As the angle increases, the force required to move the blocks also increases. This is because the weight of the blocks is acting against the force needed to move them up the ramp.

## 4. What factors influence the acceleration of the blocks on the inclined ramp connected by a pulley?

The acceleration of the blocks on the inclined ramp is influenced by several factors, including the angle of the ramp, the weight of the blocks, and the friction between the ramp and the blocks. Additionally, the mass and shape of the blocks can also affect their acceleration.

## 5. How can we calculate the force required to move the blocks on the inclined ramp connected by a pulley?

To calculate the force required to move the blocks, we can use the formula: Force = Mass x Acceleration. This equation takes into account the weight of the blocks, the angle of the ramp, and the friction between the ramp and the blocks. By plugging in these values, we can determine the force needed to move the blocks up the ramp.

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