A 1,383 kg purple car is driving southbound on a road and collides with a 1,827 kg orange car, that was traveling 31.87 m/s eastbound. The two cars collide and stick, sliding 14.54 meters before coming to rest. What was the initial velocity of the two-car system just after the collision? Take the coefficient of friction to be 0.463, and the acceleration due to gravity to be 9.8 m/s2. Answer to two decimal places.

Explanation:

We shall apply work energy theorem to calculate the initial velocity just after the collision .

Their kinetic energy will be equal to work done by friction .

force of friction = μ mg , where μ is coefficient of friction , m is total mass and g is acceleration due to gravity

force = .463 x 3210 x 9.8

= 14565.05 N

work done = force x displacement

= 14565.05 x 14.54 = 211775.88 J

now applying work energy theorem

1/2 m v² = 211775.88 , m is composite mass , v is velocity just after the collision

.5 x 3210 x v² = 211775.88

v² = 131.94

v  11.48 m /s

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the independent variable, the one that is intentionally manipulated, is whether or not the car hits the barrier.

the dependent variable, the one that you measure the response in, is the distance that the washers travel.