Physics 121
posted by Phil .
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 frictionless. 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.

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•gT2,
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 = (T1T2)•R,
ε = a/R,
I•ε =M => m•R²•a/2•R =(T1T2) •R =>
m•a/2 = (T1T2).
m1•a + m2•a = T1 + m2•g T2 = m2•g + (T1T2) = m2•g +m•a/2,
a = m2•a/[m1+m2m(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
Respond to this Question
Similar Questions

physics
A block (mass = 2.9 kg) is hanging from a massless cord that is wrapped around a pulley (moment of inertia = 1.2 x 103 kg·m2), as the figure shows. Initially the pulley is prevented from rotating and the block is stationary. Then, … 
Physics 121
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 frictionless. If the block are … 
Physic
A block (mass 2.4 kg) is hanging from a massless cord that is wrapped around a pulley 3 2 (moment of inertia of the pulley = 1.3 x 10 kg·m ), as the drawing shows. Initially the pulley is prevented from rotating and the block is … 
Physics
A block of mass m1 is on top of a block of mass m2. Block 2 is connected by an ideal rope passing through a pulley to a block of unknown mass m3 as shown. The pulley is massless and frictionless. There is friction between block 1 and … 
phy
(Q1)A 40N force applied at an angle of 37c above the horizontal pulls a 5kg box on a horizontal floor. The acceleration of the box is 3m/s2,How large a frctional force must be retarding the motion of the box. (a)50 N(b)13N(c)17N(d)25N … 
Physics
calculate the acceleration of this system, assuming that there are no frictional forces between the table and Block A. Block A is sitting on a table connected by a rope to a pulley system and Block B is hanging off the table connected … 
Physics Dynamics
A 4kg block is connected by means of a massless rope to a 2kg block. What is the magnitude of the acceleration if the coefficient of kinetic friction between the 4kg block and the surface is 0.20? 
Physics Help Needed
Two blocks are connected by massless string that is wrapped around a pulley. Block 1 has a mass m1=6.90 kg, block 2 has a mass m2=2.30 kg, while the pulley has a mass of 1.70 kg and a radius of 12.2 cm. The pulley is frictionless, … 
physics
Two blocks are connected with a light string that is hung over a pulley, as shown in the diagram to the right. One block has twice the mass of the other, and the pulley has the same mass as the heavier block. The pulley consists of … 
physics
Two blocks are connected by massless string that is wrapped around a pulley. Block 1 has a mass m1=6.50 kg, block 2 has a mass m2=2.50kg, while the pulley has a mass of 1.40 kg and a radius of 22.0 cm. When the pulley turns, there …