Mechanics

M-E1 : Rolling Track

Unit

Work and Kinetic Energy

Purpose

Illustrate work-kinetic energy theorem

Equipment

  1. Curved track on a stand
  2. Several balls to roll

Suggestions

  1. Release balls from one end and catch them when they come momentarily to rest upon return; note the initial and the final positions.
  2. Discuss the role of the height of end-points of the track, and its shape in applying W=DK theorem.
  3. Discuss the difference between the initial and final rest positions in terms of friction, and compare the rolling friction of a few balls.

Discussion

  1. Releasing the ball
  2. Ball in transit
  3. Ball reaches the other end

M-E2a : Loop-the-Loop (Large)

Unit

Mechanical Energy. Kinetic Energy of Rolling

Purpose

Illustrate work-kinetic energy theorem

Equipment

  1. Loop-the-loop track on a stand (there are two, larger is better; in both cases balls with good traction must be chosen so as to avoid sliding friction)
  2. Several balls to roll

Suggestions

  1. Release a ball from a low position on the longer side of the loop, and note that it fails to complete the run.
  2. Release a ball from near the top of the longer side, and note that it easily makes the run. 
  3. Ask what is the minimum release height. Try.
  4. Try dropping from h=2.5R (R=radius of the loop)
  5. Try dropping from h=2.7R, then a bit above that height to compensate for rolling friction.

Discussion

Prediction of h min based on translational KE alone of a ball gives h=2.5R, independent of mass and r, the radius of the ball (assuming r<<R). If rotational KE is included, prediction becomes h=2.7R. For the ball to make the loop run, one must compensate for the rolling friction. To obtain R accurately it is best to measure the diameter 2R, taking into account the position of the ball's center relative to the track. 

  1. Measuring the diameter 2r of the loop-the-loop (using two balls, from center to center)
  2. Finding the release point at h=2r
  3. The ball fails to complete the loop
  4. Finding the release point at h=2.7r+d, d approx. 3cm to compensate for the rolling friction
  5. The ball at the top of the loop on its way to complete the run

M-E2b : Loop-the-Loop (Small)

Unit

Mechanical Energy. Kinetic Energy of Rolling.

Purpose

Illustrate work-kinetic energy theorem.

Equipment

  1. Loop-the-loop track on a stand
  2. Small orange (super) ball

Suggestions

  1. Release a ball from a low position on the longer side of the loop, and note that it fails to complete the run.
  2. Release a ball from near the top of the longer side, and note that it easily makes the run.
  3. Ask what is the minimum dropping height. Try.
  4. Try dropping from h=2.5R (R=radius of the loop)
  5. Try dropping from h=2.7R, then a bit above that height to compensate for rolling friction.

Discussion

  1. Releasing the ball
  2. Ball rolls down
  3. Ball at the top of the loop on its way to competing the run

M-E3 : Twin Balls

Unit

Mechanical Energy, Collisions

Purpose

Bring into sharp focus the difference between two apparently "similar" events, one in which mechanical energy is (nearly) conserved and another in which it is not.

Equipment

Two apparently identical, small black balls, one "happy" the other "sad"

Suggestions

  1. Drop the "happy" ball on the tabletop
  2. Drop the "sad" ball on the tabletop
  3. Ask students what is different between the two collisions. Where did the mechanical energy go in the second case?

Discussion

The only difference in the appearance of the balls is that one is shinier than the other

  1. Both balls being released from the same height
  2. After the collision, "happy" ball on its way up while "sad" remains on the table.
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