Posted by **Phil** on Saturday, May 5, 2012 at 9:07pm.

Two block are connected by a rope that runs over a pulley. The block on the tables has mass 4kg, the hanging block has mass 2kg, and the pulley has mass 0.5kg and radius 0.25m. Assume that the table is friction-less. If the block are released from the rest, determine their speeds after the hanging block has dropped 0.75m.

Please explain the formula and steps. Thanks.

- Physics 121 -
**Elena**, Sunday, May 6, 2012 at 12:34pm
m1 =4 kg, m2 = 2 kg, m = 0.5 kg, R = 0.25 m, h= 0.75 m.

Projections of the equation according to the 2 Newton's law for two blocks on the horizontal (for the 1st block)and on the vertical (fot the 2nd block) axis:

m1•a = T1

m2•a =m2•g-T2,

The equation of the pulley motion (2nd Nerton's law, for the rotational motion)

I•ε =M.

The moment of inertia of the pulley (disk) is

I =m•R²/2 ,

M = torque = (T1-T2)•R,

ε = a/R,

I•ε =M => m•R²•a/2•R =(T1-T2) •R =>

m•a/2 = (T1-T2).

m1•a + m2•a = T1 + m2•g -T2 = m2•g + (T1-T2) = m2•g +m•a/2,

a = m2•a/[m1+m2-m(m/2)] =

= 2•9.8/(4+2+0.125)=3.336 m/s^2,

a = v^2/2•h ,

v=sqrt(2•a•h) = sqrt(2•3.336•0.75) =

= 2.2 m/s^2

## Answer this Question

## Related Questions

- Physics 121 - Two block are connected by a rope that runs over a pulley. The ...
- phy - (Q1)A 40N force applied at an angle of 37c above the horizontal pulls a ...
- Physics - calculate the acceleration of this system, assuming that there are no ...
- Physics Dynamics - A 4-kg block is connected by means of a massless rope to a 2-...
- physics (newton's laws) - A 5.00 kg object placed on a frictionless, horizontal ...
- Physics - Two blocks are connected by a string on a pulley. One block is on an ...
- Physics - A block of mass m1 is on top of a block of mass m2. Block 2 is ...
- physics - In the drawing, the weight of the block on the table is 428. N and ...
- Physics - In the drawing, the weight of the block on the table is 405. N and ...
- physics - A light rope is attached to a block with a mass of 6 kg that rests on ...