MOMENTUM

 We all know that a heavy truck is harder to stop than a small car moving at the same speed. We state this fact by saying that the truck has more momentum than the car. By momentum we mean inertia in motion or, to be more specific, the product of the mass an object and its velocity:

 
Momentum= mass*velocity

Or in shorthand notation

Momentum=mv

We can see from the definition that a moving object can have large momentum if either its mass or its speed is large, or if both are. A truck has more momentum than a car moving at the same speed because the truck has a greater mass. A huge ship at a low speed has a large momentum because of its high speed. A massive tuck with no brakes rolling down a steep hill has a large momentum, whereas the same truck at rest has no momentum at all because the v part of the mv is zero.

Elastic and Inelastic Collisions Explained

1) What is the significant difference, in terms of conservation of kinetic energy, between using elastic bumpers to cushion the collision and using a pin and soft plastic to couple the gliders? Describe each of the two types of collisions.

The following presumes that the duration of the events studied is so small that the effects of friction or other external forces are negligible.

A perfectly elastic bumper is not deformed by a collision.  Therefore there is no heat loss or other energy loss associated with the collision.  In a collision of two objects in which the objects bounce apart and there is no energy loss, kinetic energy and momentum both are conserved.  That is, the total momentum of the system after the collision is the same as the total momentum of the system before the collision occurred. Also, the total kinetic energy of the system after the collision is the same as the total kinetic energy of the system before the collision occurred.  This is called an elastic collision.  When two objects collide and stick together, momentum is conserved, but kinetic energy is not conserved.  This is called an inelastic collision. The kinetic energy of the system is decreased as it is transformed into other types of energy, such as heat when the soft plastic is deformed.
2) Is there a comparable difference, in terms of conservation of momentum, between the two types of collisions? What seems to be true about the effect of the collision on total momentum that differs from its effect on kinetic energy?

In elastic and inelastic collisions, there is no difference as far as conservation of momentum is concerned.  The total momentum of the system is conserved in both types of collisions.  The effect on kinetic energy is different.  The total kinetic energy of the system is conserved in an elastic collision, but not in an inelastic collision.
A. Collisions with Coupling
 

A girl, mass 70.0 kg, is running 3.0 m/s east when she jumps onto a stationary skateboard, mass 2.0 kg. What is the velocity of the girl and skateboard assuming they move off together?
Solution:

mv1 + mv2 = m(1+2)v(1+2)
(70.0 kg)(3.0 m/s [E]) + (2.0 kg)(0 m/s) = (72.0 kg)v(1+2)
v(1+2) = 2.92 m/s [E]

B. Collisions without Coupling
 

A toy truck, with mass 20.0 g, travels along a level tabletop at 0.50 m/s. A miniature car, with mass 5.00 g, speeds headlong toward the toy truck at 0.75 m/s. Immediately after the collision, the toy truck continues in its original direction at 0.10 m/s. What is the velocity of the miniature car?

Solutions:
Establishing the original direction of the toy truck as “+” and the original direction of the miniature car as therefore “-”

m1v1i + m2v2i = m1v1f + m2v2f
(20.0 g)(0.50 m/s) + (5.00 g)(-0.75 m/s) = (20.0 g)(0.10 m/s)+ (5.00 g)v2f
v2f = 0.85 m/s [in the direction of the toy truck before collision]
C. Explosions

A boy, mass 70.0 kg, riding a skateboard, mass 2.0 kg, is traveling 3.0 m/s east when he attempts to jump forward from his skateboard. If his velocity immediately after leaving the skateboard is 3.1 m/s [E], what is the velocity of t he skateboard?

Solution:
m(1+2)v(1+2) = mv1 + mv2
(72.0 kg)(3.0 m/s [E]) = (70.0 kg)(3.1 m/s [E]) + (2.0 kg)v2
v2 = 0.50 m/s [W]

Reference:

http://www.physics247.com/physics-homework-help/colinear-momentum.php