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General Physics 1

 APHY 111

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Collisions in 2D

Conservation of momentum in 2DMomentum is conserved along each axis separately:

Consider a game of billiards

If the collision is elastic we also have kinetic energy conservation.

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Example: A 1500 kg car traveling east with a speed of 25.0 m/s collides at an

intersection with a 2500 kg van traveling north at a speed of 20.0 m/s, as shown in

the figure. Find the direction and magnitude of the velocity of the wreckage after the

collision, assuming that the vehicles undergo a perfectly inelastic collision (that is,

they stick together).

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Example: In a billiard game, a player wishes to sink a target ball in the corner

pocket. If the player hit the cue ball giving to it a speed of v1i = 5 m/s, then the cueball elastically collide with the target ball which moves toward the corner pocket with

a speed of v2f 

= 3 m/s and at an angle of 35° in respect to the x-axis, as shown in

the figure. Assume that friction and rotational motion are unimportant. Note that all

balls have the same mass, the target ball is at rest before the collision (v2i

= 0), and

vif 

is the speed of the cue ball after the collision. At what angle θ is the cue ball

deflected?

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 A cannon is rigidly attached to a carriage, which can move along horizontal rails but is

connected to a post by a large spring, initially unstretched and with force constantk=2.00 x 104 N/m, as in the figure. The cannon fires a 200 kg projectile at a velocity of

125 m/s directed 45.0° above the horizontal.

(a) If the mass of the cannon and its carriage is 5 000 kg, find the recoil speed of the

cannon.

(b) Determine the maximum extension of the spring.

(c) Find the maximum force the spring exerts on the carriage.

(d) Is the momentum of this system conserved during the firing? Why or why not?

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