# Force and Energy in robots

There are two similar and hypothetical robots that move with wheels powered by motors, Robot A and Robot B.

Robot A has a gear ratio of 3:1 (The gear connected to the motor is three times larger than the gear connected to the wheel), while Robot B has a gear ratio of 1:3.

A spring balance is connected to each of the moving robots. Because of mechanical advantage caused the gears, the reading of the spring balance for Robot B should be nine times greater than Robot A.

However, Robot A moves at a speed 9 times faster than Robot B. Through the formula for kinetic energy, KE=1/2mv^2, a moving Robot A would have more kinetic energy than a moving Robot B.

Robot A has less force than Robot B, but it has greater energy than Robot B. When the two robots compete by pushing each other in a fashion of sumo, does the force or energy of the robots determine the winner? From my experience with Lego Mindstorms robotic sets, generally robots like Robot B will win. Why is that?

I'm very sorry if this question is confusing.

• Put simply: the vector sum of all Forces determines the direction of motion. Two robots pushing against each other are exerting force based on their output torques or linear force. A robot moving fast can "crash" into another; use momentum equations to determine the outcome. – Carl Witthoft Nov 13 '14 at 14:28