Motion of connected particles.

Pulleys and accelerations

To do these questions

  1. Draw the diagram, indicate the direction the system moves
  2. Draw separate diagrams of the forces on each particle
  3. Write out equations (in A) for each particle
  4. Net Force = Forces w/ A - Forces vs A
  5. Combine the equations

Look at the diagram below and you might start to understand what we are dealing with here. There are 2 masses connected to each other by a light (massless) inextensible string. The string is connected to the particles over a frictionless pulley (which means it can turn freely with no acceleration loss).

The system is at rest at the moment, what forces are each particle experiencing ?

Draw a diagram for each particle and show what forces are working on the particle.

The system is released from rest, what will happen ?

The 5kg mass will fall towards the ground, what will happen the 2kg mass? Can it fall to the ground? What forces operate on the system?

The T's represent the tension in the string, can the tension be greater at one end of the string than at the other end ?

So the tensions must be the same (in this example). The System moves, back to Newtons 1st law, what causes motion ..... a force.

How do we measure a force F = ma. So the forces on the mass lead to a Net force which causes the blocks to accelerate. If we combine (add up) the forces we find this lets us find the acceleration on the block.

5kg mass

Goes down, let Net Force & a be positive

W - T = F

5g - T = 5a

2kg mass

Goes up let Net Force & a be negative

W - T = - F

T - W = F

T - 2g = 2a

The tensions are the same so lets combine these 2 answers

5g - T + T - 2g = 5a + 2a

5g - 2g = 7a

3g = 7a

a = 3/7g

The key is that the greater mass will go down but that both particles will have the same magnitude of acceleration but in opposite directions.

To demonstrate what happens try out the 5 minute pass here

more here on problems with 2 different strings

Bodies on tables ...