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

ID: 1884136 • Letter: 1

Question

1. Two cars collide at an icy intersection and stick together afterward. The first car has a mass of 1400 kg and was approaching at 9.00 m/s due south. The second car has a mass of 750 kg and was approaching at 17.0 m/s due west.

(a) Calculate the final velocity 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 is positive)

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

Explanation / Answer

a).

let the final velocity of the cars be v.

from conservation of momentum in vertical direction;

initial momentum of 1st car in vertical direction +initial momentum of 2nd car in vertical direction = final momentum of both cars in vertical direction

=> 1400*9 + 750*0 = (1400+750)*Vy

=> Vy = 5.86 m/s (towards south)


from conservation of momentum in horizontal direction;

initial momentum of 1st car in horizontal direction +initial momentum of 2nd car in horizontal direction = final momentum of both cars in horizontal direction

=> 1400*0 + 750*17 = (1400+750)*Vx
=> Vx = 5.93 m/s (towards west)

total final velocity = sqrt(5.932 + 5.862) = 8.33 m/s

b). direction = tan-1(5.86/5.93) = 44.65 degrees counterclockwise from west = +44.65 degrees

c). K.E. lost = initial K.E. - final K.E.

=> K.E. lost = [(0.5*1400*92) +(0.5*750*172)] - [0.5*(1400+750)*8.332] = 90481.93 J