Two frictionless tracks A and B span the same horizontal distance, however track

Question

Two frictionless tracks A and B span the same horizontal distance, however track B has a dip of vertical depth h. The tracks are equipped with identical springs of spring constant k for launching identical balls of mass m. Before the launch, the balls are just touching the springs, which are compressed by an amount X. The balls are free of the springs when they have crossed the x=0 position. We want to determine which ball crosses the x=d position first.

a) Which of the balls do you expect to be faster at position x=d/2?

1) The ball on track A

2) The ball on track B

3) both have the same speed

b)Which of the balls do you expect to be faster at position x=d?

1) The ball on track A

2) The ball on track B

3) both have the same speed

c)Which principle allows you to determine the speed of balls at d/2 and d?

d)For each track, derive expression for the speed of the ball at position x= d/2 and position x=d.

e) Which ball crosses the x=d position first?

Explanation / Answer

a) 2) The ball on track B b)2) The ball on track B c) acceleration due to gravity e) both cross at the same time

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