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.
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
The equation of the pulley motion (2nd Nerton's law, for the rotational motion)
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
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
A block with mass m1 hangs from a rope that is extended over an ideal pulley and attached to a second block with mass m2 that sits on a ledge. The second block is also connected to a third block with mass m3 by a second rope that
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
A marble block of mass m1 = 500.1 kg and a granite block of mass m2 = 237.4 kg are connected to each other by a rope that runs over a pulley, as shown in the figure. Both blocks are located on inclined planes with angles á = 35.3
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
A 4-kg block is connected by means of a massless rope to a 2-kg block. What is the magnitude of the acceleration if the coefficient of kinetic friction between the 4-kg block and the surface is 0.20? Note : The 4kg block is on the
A rope connects a 40 kg block to a 30 kg block. The rope passes over a pulley at the top of a 37° incline. The 40 kg block rests on the incline and the 30 kg block hangs from the pulley. Calculate the acceleration of either
A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg, frictionless pulley. A constant 10 N tension is applied to the other end of the rope. Starting from rest, how long does it take the block to move 30 cm?
In the system shown in the figure , block A has mass m_A = 2.08 kg, block B has mass m_B = 0.370 kg, and the rope connecting them has a nonzero mass 0.203 kg. The rope has a total length 1.03 m and the pulley has a very small
A block of mass 2.30kg is accelerated across a rough surface by a rope passing over a pulley. a) The tension in the rope is 12.4N, and the pulley is 11.2cm above the top of the block. The coefficient of kinetic friction is 0.415.