POTW

Below are PoTWs (Problems of the Week) created for members of the Harker Physical Sciences Club by our officers. We've added them onto this website so you can give them a try too!

POTW #1 (Week of 2/24)

Five snails are placed at the vertices of a regular pentagon with side length d. Each snail follows the snail to its right with a constant speed v. How long does it take for all the snails to reach the center of the pentagon?

Solution:

By symmetry, all snails will reach the center at the same time. Since they all reach the center at the same time, the time it takes for the snails to reach the center is also the time for any snail to catch up to the snail ahead of him. Again, by symmetry, each snail rotates with the same angular velocity. Therefore, we can go into the reference frame of one of the snails, and we will find that the snail to its left is moving towards it with a speed of v(1-cos(72°)). The time it takes for the left snail to reach the snail whose reference frame was chosen is d/(v(1-cos(72°))), which is also the time it takes for all snails to reach the center.

POTW #2 (Week of 3/3)

Jacqueline has a cubical box, with side length s, half-filled with a liquid of density p. She accelerates the box to the right with acceleration g. Find the pressure on the bottom-left edge.

POTW #3 (Week of 3/10)

N identical balls are placed in a row constrained to move in one dimension, which lies along the line containing the N balls. If all collisions between balls are elastic, and the balls are set off with set initial velocities, what is the greatest number of collisions that could happen?

An elastic collision between two identical balls looks equivalent to the balls passing through each other (as if the balls had switched identities). If the leftmost ball has the greatest velocity to the right and each ball has less rightward velocity than the ball to its left, each ball will be able to pass through all the balls to its right, and that gives us choose 2 collisions = N*(N-1)/2.

POTW #4 (Week of 3/17)