John has just received a new dart gun,and he wants to practice his aim. Assume h

Question

John has just received a new dart gun,and he wants to practice his aim. Assume his dart gun can carry 6 darts, each with a mass of 18 g, and that the darts exit the gun at a speed of 440 m/s. John's fires and hits a 0.5 kg can of corn. The dart passes through the can of corn, exiting the can with a speed of 180 m/s, moving horizontally the entire time. The impact sends the can sliding along a flat horizontal shelf. If the coefficient of kinetic friction between the can and the shelf is 0.35, how far does the can slide before coming to rest (in meters)?

Explanation / Answer

Let's look at conservation of momentum. Initially the can is at rest so all the momentum is that of the darts. (.018)(440)

After the momentum is the sum of the can and the darts (0.18)(180) + (0.5)(v) where v is the velocity of the can. They must equal each other.

(.018)(440) = (0.18)(180) + (0.5)(v) ; v=9.36m/s

So when the can starts sliding it has a kinetic energy of (0.5)(0.5)(9.36)2 = 21.9J The can then comes to a rest and has zero energy. All of the energy went to friction... so friction did 21.9J of work.

The normal force of the can is equal to the weight so it is (0.5)(9.8) = 4.9N. The coefficient is given as 0.35

Friction force = 4.9*0.35 = 1.715N

Work = force*displacement. We know the work and and force here.

21.9 = (1.715)(x) where x is how far the can traveled. x = 12.8m

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