Kinetic Energy Questions - All Help Appreciated?

1.) If a system has zero momentum, does it necessarily have zero kinetic energy? What is an example to illustrate this answer?

2.) A sports car with a mass of 1200 kilograms travels down the road with a speed of 20 meters per second. Why cant we say that its momentum is smaller than its kinetic energy?

Thank You All!

1.) If a system has zero momentum, does it necessarily have zero kinetic energy? What is an example to illustrate this answer?

Momentum p = mv; so that v = p/m = 0/m = 0 when there is zero momentum p = 0. Therefore, KE = 1/2 mv^2 = 1/2 m0^2 = 0. Therefore, yes, if p = 0 then KE = 0 as well.

2.) A sports car with a mass of 1200 kilograms travels down the road with a speed of 20 meters per second. Why cant we say that its momentum is smaller than its kinetic energy?

Makes no sense, for one thing. That's comparing apples to oranges, momentum and KE are not the same thing. They don't have the same units of measure. p units are kg-m/sec^2 but kinetic energy is kg (m/sec)^2.

We could make the argument that momentum is embedded in kinetic energy. For example, KE = 1/2 mv^2 = 1/2 pv Thus, p, momentum, is just one factor in KE; so p < KE. But, and this is a big BUT, that's still comparing apples to oranges and not really meaningful.

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