Mechanics

M-S1 : Diatomic Particle

Unit

Center of Mass

Purpose

Illustrate the usefulness of the center of mass to describe oscillatory motion of two masses

Equipment

  1. PASCO 1m track
  2. Two carts connected by a spring
  3. CM marker, assorted weights

Suggestions

Demonstrate CM for:

  1. Uniform motion, no oscillations
  2. Oscillating masses with CM stationary
  3. Combined motions 1 & 2
  4. Optional: oscillations with one mass held at rest (how does the frequency change?)
  5. Optional: redo 3 varying the loads on carts

Discussion

Compressing the spring is a bit of a fine art; excessive compression will cause a deformation of the spring.

  1. Spring coupling of the two carts
  2. The entire set-up, with the cars oscillating at the instant the spring is compressed
  3. Close-up of the carts with the spring at its natural length
  4. Extra 1kg on the left cart, spring compressed
  5. Extra 1kg on the left cart, spring stretched

M-S2 : Hacky Sacks

Unit

Center of Mass

Purpose

Show how CM can simplify the description of motion

Equipment

  1. Dumbbell model (two balls of different size and mass connected by a rigid light rod) OR
  2. Two unequal hacky sacks connected by a string
  3. CM marker

Suggestions

Discuss motion of CM and motion relative to CM for

  1. Dumbbell dropped from rest
  2. Rotation with one mass at the center
  3. Dumbbell thrown spinning in the air

Discussion

For cases 1 and 3, the center of mass moves like a projectile as if it were a point particle of mass equal to the total mass of the system.

  1. Hacky sacks with the CM marker
  2. Dropping the hacky sacks aligned vertically
  3. In flight, with the CM marker describing a parabola and the two sacks rotating about it.

M-S3 : Quintuple Pendulum

Unit

Elastic Collisions

Purpose

Illustrate the exchange of momenta in elastic collision of equal masses

Equipment

  1. Small quintuple pendulum OR
  2. Large quintuple pendulum

Suggestions

  1. Collision of two balls (other drawn aside)
  2. Collisions of three balls (three possiblilities)
  3. Collisions of four balls (five possibilities)
  4. Collisions of five balls (six possibilities)

Discussion

Two equal masses colliding elastically exchange their linear momenta; if one is at rest before a collision, the second will be at rest after the collision. Collisions involving three or more balls can be understood by considering a series of two-mass collisions. 

  1. Equipment and set-up
  2. Two balls with remaining three tucked away
  3. After an elastic collision between two balls
  4. Five ball system: two balls are ready to be released
  5. Five ball system: after the collision in #4
  6. Two balls released from opposite directions, after the collision, with a stationary ball in the middle.

M-S4 : Collision Cars

Unit

Linear Momentum

Purpose

Test momentum and kinetic energy conservation in elastic and completly inelastic collisions

Equipment

  1. Two PASCO cars
  2. One-meter PASCO track
  3. Accessories (end-stops,...)
  4. Assorted weights

Suggestions

  1. Completely inelastic collision, equal masses
  2. Completely inelastic collision, unequal masses
  3. Elastic collision, equal masses
  4. Elastic collision, unequal masses

Discussion

For the inelastic collision the carts should face each other with their velcro ends. After, turning both carts around they will face each other with their magnet ends allowing for an elastic collision. 

  1. Before inelastic collision, equal masses
  2. Just after inelastic collision, equal masses
  3. Before the elastic collision, equal masses
  4. Just before the elastic collision, equal masses
  5. Just after the elastic collision, equal masses
  6. Elastic collision, unequal masses
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