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Title : Conservation of Linear Momentum Apparatus : Science Workshop Interface 750 Motion Sensor ( PASCO Model CI 6742 ) 2 Dynamics Cart 2 Laboratory jack Runway Mass ( 1 set ) Metre rule Triple Beam Balance or Digital Balance Objective : How does the total momentum of two carts before collision compare to the total momentum of two carts after the collision ? Theory : The principle
of Conservation of momentum
For
a system of interacting objects, the total momentum remains constant, provided
no external resultant force acts on the system. Total initial momentum = total final momentum For two-object collision, momentum conservation is easily stated mathematically by the equation :
Note
that momentum is a vector.
(i) It holds true
no matter what kind of forces the bodies exert on each other. They may be
gravitational forces, electric or magnetic forces, tension in strings,
compression in springs, attraction or repulsion.
(ii) It does not matter
whether the bodies stick together or scrape against each other or bounce apart.
They do not even have to touch. When two strong magnets repel or when an alpha
particle is repelled by a nucleus, conservation of momentum still holds.
Collision between particles is a very important tool in the study of nuclei and
elementary particles.
(iii) The
law is not restricted to systems of only two objects; there can be any number of
objects in the system.
(iv) The
law applies to a galaxy as well as to an atom.
(v) The law applies to two
dimensional collisions. Compare the total momentum of the two carts before collision to the total momentum of both carts after collision. Procedure : Connect the interface to the computer, turn on the interface, and turn on the computer. Connect one Motion Sensor into Digital Channels 1 and 2 on the interface. Connect the yellow plug into channel 1 and the other plug into channel 2. Connect the second Motion Sensor into Digital Channels 3 and 4 on the interface. Connect the yellow plug into channel 3 and the other plug into Channel 4. Sensor Calibration Place one Motion sensor exactly one meter away from a target. Arrange the sensor and target so the pulses from the sensor can reflect from the target and be detected by the sensor. Set Calibration distance =1 m. Click the 'Calibrate' button in the Motion Sensor Window. ( For the second Motion Sensor, set the Calibration distance = -1 m ) Equipment Setup : Place the runway ( track ) on a horizontal surface. Level the track by placing a cart on the track. ( Use the adjustable feet at one end of the track to raise or lower that end until the cart will not roll one way or the other. ) Use the Triple Beam Balance to find the mass of each cart. Place a cart at each end of the track. Let the cart on the left be 'cart 1' and the cart on the right be 'cart 2'.
Carry out the experiment according to the following different situations. Elastic collision 1. Equal mass and equal speed 2. Equal mass, one cart moving and one cart stationary 3. Loaded cart moving at low speed and unloaded cart moving at high speed. 4. Loaded cart moving and unloaded cart stationary 5. Loaded cart moving at high speed and unloaded cart moving at low speed. Inelastic collision 6. Equal mass, same speed 7. Equal mass, one moving and one stationary Explosion 8. Equal mass 9. Unequal mass
Data Recording : (I) Equal mass collision
Data Analysis : Elastic collision 2. Equal mass, one cart moving and one cart stationary 3. Loaded cart moving at low speed and unloaded cart moving at high speed. 4. Loaded cart moving and unloaded cart stationary 5. Loaded cart moving at high speed and unloaded cart moving at low speed. Inelastic collision 7. Equal mass, one moving and one stationary Explosion 8. Equal mass 9. Unequal mass
Application of principle of conservation of momentum: 1. You jumps off a rowing boat. Your jump to the safety of the dry ground pushes the boat backwards so the boat recoils - sometimes with disastrous consequences. Take care if you ever try it ! The momentum carried away by you is equal and opposite
to that
carried away by the boat.
Discussion 1. How does the total momentum of two carts before collision compare to the total momentum of two carts after the collision ? 2. What are the precautions of this experiment ? 3. Account for the sources of error in this experiment.
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