Multiple Masses

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Multiple Masses
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Tension in Ropes and Cables

• When a crane exerts a force on one end of a
  cable, each particle in the cable, exerts an
  equal force on the next particle in the cable.
  This creates tension throughout the cable
• Tension magnitude of the force exerted on or by
  a cable, rope, or string

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Assumptions

• 1. mass of the rope or cable is very small and
  therefore we ignore compared to the load and does
  not affect motion
• 2. tension is the same at every point in a rope
  or cable
• 3. If the rope or cable passes over a pulley, the
  direction of the tension changes but the
  magnitude stays the same. (pulley is frictionless
  and its mass is negligible)

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Connected Objects

• Elevators are not simply suspended from cables.
  Instead the supporting cable passes over a pulley
  and then back down to a heavy, moveable
  counter-weight. Gravitational forces act downward
  on the counter-weight creating tension in the
  cable. The cable then exerts an upward force on
  the elevator

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Atwood Machines

• George Atwood (1745-1807) built a machine he used
  to determine the value of g

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Assigning Direction to the Motion of Connected
Objects

• With the Atwood machine the masses are moving in
  different direction but connected objects move as
  a unit
• The connecting coble or rope changes only the
  direction of the forces acting on the objects and
  has no effect on the magnitude of the forces. You
  can assign the direction of the motion as being
  from one end of the cable or rope to the other
• Se figure 10.12 page 482

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• When working with a group of connected objects we
  call it a system. The forces exerted through a
  rope or cable are called internal forces
• The forces that affect the motion of a system are
  known as external forces (gravity, friction)

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Objects Connected at an Angle

• In the lab, a falling weight is often used to
  provide a constant force to accelerate dynamic
  carts. Gravitational forces act downward and the
  string exerts a horizontal force on the cart

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Steps for Problem Solving

• Analyze the forces on each individual object
  (FBD)
• Assign a direction to the motion
• Draw the connecting string or rope as though it
  was a straight line
• Draw a FBD for the resulting system
• Use Newtons 2nd Law to calculate acceleration