Biology Forums - Study Force

 I want to explore what kinetic energy means. In this case, let's take two objects with about the same kinetic energy. A 94 lb (42.6 kg) cheetah running at 14 m/s (well within it's capability) and a rather powerful 23 gram bullet going at 602 m/s. What would happen if the cheetah runs straight into a 180 lb man? What would happen if the bullet hits a 180 lb man wearing a bullet proof vest? Let's assume the bullet doesn't exit, so all energy is transferred into the armor. What happens to the energy of the objects as they strike their targets? Use the physics knowledge you've gained so far in these three chapters to answer these questions.

(As wikipedia says) The kinetic energy of an object is the energy which it possesses due to its motion.
If an item with mas m moves with spped u, then the kinetic energy is (1/2)mu2

To solve these problems you need to use momentum.
The momentm of a moving item is: P=m*u (P is momentum, m is the mass of the item and u is the velocity of the item.)
If you have more than one item at your system, then the total momentum is the vector addition of the momentums of each item.
The units of the momentum doesn't really matter, you can use the units of mass and velocity (for example kg*m/s or lb*m/s)

At isolated systems, the total momentum of the system doesn't change (for example, after a collision). (To solve these problems we assume that the system is isolated.)

Now, for your exercises:

A cheetah with m1=94lb=42.6kg is running with u1=14ms at a man with m2=180lb=81,6kg, who is standing still (u2=0)

Before the collision (of the cheetah with the man) the momentum of the cheetah-man system was:
P=P1+P2=m1*u1+m2*u2=42.6*14+81.6*0=596.4kg*m/s (direction same as u1)

After the collision, we assume that the cheetah and the man has "stuck together" and move like one single item. (it isn't stated clearly, but I think that is how it must be solved)
As we said, after the collision the momentum of the system remains the same. So, the final momentum will be: P=(m1+m2)*u=596.4    (u is the velocity of the "cheetah-man" item, because as we said now the cheetah and the man moves like one thing)
(m1+m2)*u=596.4 from there we easily find the final velocity. u=4.8m/s.
Now, if you compare the new kinetic energy of the cheetah-man item [(1/2)*(m1+m2)*u] and the separated kinetic energy of the cheetah before the collision [(1/2)*m1*u1] you will see that a part of the kinetic energy is lost. This part of energy was transformed into heat.


Exactly the same must be dome with the second problem:
Answer of the 2nd problem: