Connected Particles

• If you have two objects, A and B, with A on top of B, and B on the floor, what are the forces involved?

  
  

  1. A's weight pushing down on B
  2. Normal reaction of B pushing on A
  3. B's weight pushing down on the floor
  4. Same normal reaction as 2. of A pushing down on B
  5. Normal reaction of the floor pushing up on B

  
• Normal reaction: An object at rest on a surface exerts a force on the surface. The reaction force acts at right angles to the surface
• When a particle of mass m is resting on the floor, what is the normal reaction from the floor equal to?

  mg
• What does particle A experience when particle B is resting on top of it?

  • The normal reaction from the weight of B
  • NOT the weight of B
• Particles moving forward typically have a driving force and incur friction
• When one particle is pulling another forward, it experiences tension from the connection
• If a particle is being pulled forward, tension pulls it forward, and friction resists the motion
• A stationery pulley with weights on either side, experiences tension on both sides and an equal normal reaction going up
• Both weights on either side of a stationery pulley experience tension pulling them up, and $mg$ pulling them down

  
• What forces are acting upon A?

  • tension pulling up the slope
  • weight pulling down
  • friction resisting the motion upwards
  • normal reaction pushing at right angles to the slope

  
• How do you resolve the weight of A into its component parts?

  • $mg\cos\theta$
  • $mg\sin\theta$

  
• What forces are acting upon B ?

  • tension pulling up
  • weight pulling down

  
• If the angle at the bottom left is $\theta$ , what is the angle at the top right?

  $90\ -\ \theta$

  
• How do you calculate the resultant force on the pulley?

  1. Calculate the angle at the top right
  2. Halve it
  3. Take cos of the result
  4. Multiply by the total tension (which is 2T)

  
• General method for solving connected particles questions:

  1. Do F = ma twice
  2. Simultaneous equations - typically to find out what the acceleration and tension are
  3. Typically there will be a change of state, like a string breaking. Use SUVAT to find out v (which will become u when the string breaks)
  4. Calculate the new acceleration at T=0
  5. Another SUVAT, use new acceleration, value of u will be v from before