# ASK A SCIENTIST

**Date: 03-28-2012**

**Question:**How many pounds of force would it be if a 600-pound sumo wrestler tackled a 100-pound kid?

**Answer:**

Oh my, that would be a horrible situation for that poor kid. But I believe you asked this question from a purely scientific viewpoint, so let's calculate the force using concepts and tools developed in classical mechanics (which is one of the foundations of physics).

Classical mechanics tells us two fundamental laws of nature that are quite useful in answering your question. One is conservation of momentum, and the other conservation of energy. Momentum of a moving object is how hard it is to stop it and determined by the object's mass times its speed. Kinetic energy of a moving object (how much work it can do to other objects) is given by half of its momentum times its speed.

Let's assume that the 100-pound kid is standing still, and the 600-pound sumo wrestler is running toward him at the speed of 10 mph (miles per hour). The kid's momentum and kinetic energy are both zero, while the wrestler's momentum and kinetic energy are 600 x 10 = 6,000 [pound mile/hour] and 6,000 / 2 x 10 = 30,000 [pound mile^{2}/hour^{2}], respectively, before the tackle.

When the wrestler tackles the kid (ouch!), some of the wrestler's momentum and kinetic energy are transferred to the kid, so he starts moving too, but how fast? Unlike football, sumo wrestlers don't necessarily hold on to their opponents when they tackle, so the kid's speed will be different from the wrestler's. Therefore, there are two unknown numbers here - the speed of the kid and the speed of the wrestler, after the tackle.

But thanks to the two conservation laws, we can write two equations, letting the sum of their new mometa equal 6,000 and the sum of their new kinetic enegies equal 30,000. (Actually, the latter statement is not accurate, because energy escapes in various forms such as heat and sound. But let's ignore this for now.). Once you learn algebra, you will be able to solve these equations yourself, but here I have already solved it for you. The solution is, the kid's speed after the tackle is about 17 mph, while the wrestler slows down to about 7 mph.

Now we are close to the final answer. The kid's momentum increased from zero to 100 x 17 = 1,700 [pound meter/second]. The change of momentum is called an impulse in classical mechanics, which equals the force applied to the object times how long the force is applied. So, if the tackle took place in just 0.1 second, the force the kid received was 760 / 0.1 = 7,600 {pound meter/second^{2}]. As one "pound force" is technically 9.8 pound meter/second^{2}, the final answer to your question is, 7,600 / 9.8 = 775 pound force. Wow. This level of shock would not be fatal, but one may faint and get some injuries.

Bottomline: Don't mess with a 600-pound sumo wrestler.