## USAYPT 2024 Problems

#### Inelastic Magnetic Collisions

Magnetic dynamics carts are often used to show both elastic, and inelastic, collisions. While in the inelastic case the abutting magnets collide and stick together, in the elastic case they repel magnetically without touching.

Modify your school's dynamics carts to collide inelastically without actually touching each other in the process. Clearly show that momentum is continuously conserved, and explain how the excess kinetic energy is dissipated.

#### The Surface of the Moon

Mountain heights, and crater depths, on the moon's near side have been calculated since the 17th century. Now, anyone with a cell phone camera and a small telescope can photograph the moon to resolutions on the scale of kilometers.

Image the moon using standard equipment, and make a three dimensional map of its surface.

#### Bouncing Drops of Water

When water drops bounce on a flat surface, symmetry suggests that they do not spin, but rather bounce and splash. However, when bouncing on a surface with an asymmetrical pattern, they can both bounce and spin.[1]

Investigate the bouncing of water droplets both experimentally and physically.

#### Long Jumping with Weights

In Ancient Greece, athletes employed hand-held weights or halteres to extend the range of the standing long jump. In a brief 2002 article in Nature[2], Minetti and Ardigo found that archaeological halteres were in the mass range that optimized one potential benefit of the weights. The halteres may also have been hurled while the athlete was in flight.

Consider all the effects of hand-held weights in the standing long jump, where the goal is to optimize horizontal distance traveled in one leap before striking the (horizontal) ground, from both a theoretical and experimental basis.