Kinetic energy K is energy associated with the state of motion of an object. The faster the object moves, the greater is its kinetic energy. When the object is stationary, its kinetic energy is zero.
For an object of mass m whose speed v is well below the speed of light,
For example, a 3.0 kg duck flying past us at 2.0 m/s has a kinetic energy of 6.0 kg · m2/s2; that is, we associate that number with the duck’s motion.
The SI unit of kinetic energy (and every other type of energy) is the joule(J), named for James Prescott Joule, an English scientist of the 1800s. It is defined directly from Eq. 7-1 in terms of the units for mass and velocity:
Thus, the flying duck has a kinetic energy of 6.0 J.
In 1896 in Waco, Texas, William Crush parked two locomotives at opposite ends of a 6.4-km-long track, fired them up, tied their throttles open, and then allowed them to crash head-on at full speed (Fig. 7-1) in front of 30,000 spectators. Hundreds of people were hurt by flying debris; several were killed. Assuming each locomotive weighed 1.2 × 106 N and its acceleration was a constant 0.26 m/s2, what was the total kinetic energy of the two locomotives just before the collision?
Solution: One Key Idea here is to find the kinetic energy of each locomotive with Eq. 7-1, but that means we need each locomotive’s speed just before the collision and its mass. A second Key Idea is that, because we can assume each locomotive had constant acceleration, we can use the equations in Table 2-1 to find its speed v just before the collision. We choose Eq. 2-16 because we know values for all the variables except v:
With v0 = 0 and x − x0 = 3.2 × 103 m (half the initial separation), this yields
(about 150 km/h).
A third Key Idea is that we can find the mass of each locomotive by dividing its given weight by g:
Fig. 7-1 The aftermath of an 1896 crash of two locomotives.
Now, using Eq. 7-1, we find the total kinetic energy of the two locomotives just before the collision as
Sitting near this collision was like sitting near an exploding bomb.
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