1. Tension

2. Tension Forces  A taut rope has a force exerted on it.  If the rope is lightweight and flexible the force is uniform over the entire length.  This force is called tension and points along the rope. m forces on the block FNFN F fr F rope FgFg m forces on the rope FTFT -F T F rope = -F T by the law of reaction

3. Tension or Normal Force  Tension and normal forces are different. A pull on an object  tensionA pull on an object  tension A push from a surface  normal forceA push from a surface  normal force  Either one or both may be present. m Normal force FNFN F fr FgFg Tension force FTFT

4. Coupled Motion  Objects linked by tension move together Same velocity and acceleration  Tension may not be the same on two ropes F T2 = F fr2 F T1 = F fr1 + F T2 = F fr1 + F fr2 m2m2 F fr1 FT1FT1 FT2FT2 m1m1 F T2 F fr2 v 1 = v 2 v2v2

5. Pulley  A pulley uses tension to transfer a force to another direction. m1m1 m2m2 m1m1 m1m1 m2m2 m2m2 F rope F fr F rope FgFg FTFT FTFT forces on block 1forces on block 2 forces on the rope

6. Pulley Acceleration  The normal force on m 1 equals the force of gravity.  The force of gravity is the only force on m 2.  Both masses must accelerate together. m1m1 m2m2 F rope F fr  Consider two masses linked by a pulley m 2 is pulled by gravitym 2 is pulled by gravity m 1 is pulled by tensionm 1 is pulled by tension frictionless surfacefrictionless surface

7. Atwood’s Machine  In an Atwood machine both masses are pulled by gravity, but the force is unequal.  The heavy weight will move downward at (3.2 - 2.2 kg)(9.8 m/s 2 )/(3.2 + 2.2 kg) = 1.8 m/s 2.(3.2 - 2.2 kg)(9.8 m/s 2 )/(3.2 + 2.2 kg) = 1.8 m/s 2.  Using y = (1/2)at 2, it will take t 2 = 2(1.80 m)/(1.8 m/s 2 ) t = 1.4 s.t = 1.4 s.

8. Mechanical Advantage  With more than one pulley the force needed to lift an object can be reduced.  The pulley is a simple machine.  The mechanical advantage to the left is 2. next