Monday January 24, 2011. Ch 9.1 Impulse and Momentum. What is Momentum ?. Momentum (p) = mass x velocity A really slow moving truck and an extremely fast roller skate can have the same momentum. 1 kg. 10 m/sec. 1000 kg. .01 m/sec. Question :.
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Impulse and Momentum
.01 m/secQuestion :
FΔt = mΔv
F∆t = p2-p1
Ft = change in
Ft = change in
Impulse is related to the change
in its momentum.
F∆t = p2 – p1
To find the change of the momentum after a collision, solve for P2
Signs (directions) are VERY important when calculating momentum and velocity.
Force changes momentum whereas Torque changes angular momentum.
Conservation of Momentum
Condition 1: A system that does not change its mass is considered a closed system. All of these forces are internal.
Condition 2: When the net external force on a closed system is zero it is called an isolated system.
Momentum transfer from one
Object to another . Example:
Billiard ball collisions.
Is a Newton’s cradle like the one
Pictured here, an example of an
elastic or inelastic collision?
Page 210; 7-12
Momentum before the explosion is equal to momentum after the explosion
MaV = - MbV
A cart with a mass of 3 kg is sitting next to a cart with a mass of 2 kg. Between them is a compressed spring. When the spring is released, the 3 kg cart moves at a speed of 5 m/s. How fast did the 2 kg cart move?
System 2: (2 kg)(V) = 2V
Pa = -Pb
-15 = -2V
V = 7.5 m/s
An astronaut at rest in space fires a thruster pistol that expels 50g of hot gas at 750 m/s. The combined mass of the pistol and the astronaut is 80 kg. How fast and in what direction is the astronaut moving after firing the pistol?
System 2 = astronaut and pistol (80 kg)(V)
-astronaut is moving to the right.
Pa = - Pb
So… -37.5 = - 80(V)
V = 0.468 m/s
Conservation of energy and momentum can also be used to analyze collisions in two or three dimensions, but unless the situation is very simple, the math quickly becomes unwieldy.
Here, a moving object collides with an object initially at rest. Knowing the masses and initial velocities is not enough; we need to know the angles as well in order to find the final velocities.
5. Apply momentum conservation; there will be one equation for each dimension.
8. Check units and magnitudes of result.
The law of conservation of momentum applies to 2-Dimensional momentum in the same way: The momentum before is equal to the momentum after the collision.
- If you define the x-axis to be in the direction of the initial momentum, the y-component of the initial momentum is zero. Therefore the sum of the final y-component must be zero.
PA2y + PA2y = 0
or PA2y = -PA2y
Pa1 = Pa2X + Pa2X
In order to solve for the final momentum of the system, you add the momentums of both objects like you add vectors.
Pa + Pb = P2
P2 is the resultant vector
A 3 kg ball, A, is moving at a speed of 5 m/s. It collides with a stationary ball, B, of the same mass. After the collision, ball A moves off in a direction 30 degrees to the left of its original direction. Ball B moves 90 degrees to the right of ball A’s final direction. How fast are they moving after the collision?
A 1500 kg train is moving North at 23 m/s and collides with a 2000 kg train moving east at 15 m/s. They stick together. In what direction and with what speed do they move after the collision?
17 and 18