Two cars collide at an icy intersection and stick together afterward. The first

Question

Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1300 kg and was approaching at 9.00 m/s due south. The second car has a mass of 700 kg and was approaching at 17.0 m/s due west.

(a)

Calculate the final velocity (magnitude in m/s and direction in degrees counterclockwise from the west) of the cars. (Note that since both cars have an initial velocity, you cannot use the equations for conservation of momentum along the x-axis and y-axis; instead, you must look for other simplifying aspects.)

magnitude...................................... m/s

direction.................................................. ° counterclockwise from west

(b)

How much kinetic energy (in J) is lost in the collision? (This energy goes into deformation of the cars.)

..................................J

Explanation / Answer

a)

By Conservation of momentum in x-direction is

(M1+M2)Vx =M1V1x+M2V2x

(1300+700)Vx =0+700(17)

Vx=5.95 m/s

In Y-Direction

(M1+M2)Vy =M1V1y+M2V2y

(1300+700)Vy=1300(9)+0

VY=5.85 m/s

Magnitude

V=sqrt(5.952+5.852)=8.344 m/s

direction

o=tan-1(5.85/5.95)=44.5o south of west

b)

Kinetic energy lost in collision is

Klost =(1/2)*1300*92+(1/2)*700*172-(1/2)*(1300+700)*8.3442

Klost =84175 J

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