## One Mass Dropped, One Mass Flung, a Question of Kinematics - Question of the Week 3/24-3/28

Two square balls are mounted as shown on the apparatus pictured below.   When the system is tripped the ball at the left is released from rest and falls downward; ball at the right is projected horizontally and falls to the floor in a parabolic arc.

The question for this week involves how fast the two balls will fall to the floor.  In particular, after one is released and the other projected horizontally, which ball will win the race to the floor: the falling ball, the projected ball, or will the race end in a tie.  The falling ball might get to the floor first because it will travel a shorter distance.  On the other hand, the projected ball might get to the floor first because it starts with more kinetic energy, and it will therefore go faster.

When the apparatus is tripped, sending the balls on their respective paths to the floor:

• (a) the ball released from rest will arrive at the floor first.
• (b) the ball projected horizontally will get to the floor first.
• (c) the two balls will get to the floor simultaneously.

The answer is (c): the two balls will get to the floor simultaneously, as can be seen in an mpeg video by clicking your mouse on the photograph below.

The dropped ball falls to the ground, a distance of x, in a time t determined by the equation for motion in one dimension with constant acceleration, the acceleration of gravity g:

x = (1/2) g t**2

The projected ball starts with a horizontal velocity, but no vertical velocity, so its vertical component of motion is exactly the same as that of the dropped ball.  This property of motion is referred to as "separation of components."

Use your mouse to move the video frame-by-frame so that you can see in more detail how the balls fall with the same vertical position at all times.

Note the use of the "square ball," invented by Bill Norwood of the University of Maryland, so that when the balls land on the floor they will not roll away and become lost.