(a) can a single object have kinetic energy but no momentum? (b) can a system of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero? account for your answers.

(a) Can a single object have kinetic energy but no momentum? No, it can't

(b) Can a system of two or more objects have a total kinetic energy that is not zero but a total momentum that is zero? Yes, it can

Explanation:

(a) No,

as we know, the equation for the momentum (P) of single object is

P = mv

where

P = momentum (kgm/s)

m = Mass (kg)

v = speed (m/s)

and the kinetic energy (KE) of single object is

KE =

KE = kinetic energy

m = mass (kg)

v = speed (m/s)

thus, the momentum cannot be zero if it has kinetic energy since kinetic energy is proportional to the square of velocity and momentum is proportional to the velocity.

(b) yes

the two or more object is able to have kinetic energy but zero momentum. for example, two identical object move with the same velocity but different direction resulting in the total momentum to be zero.

P = mv + (-mv) -> opposite direction

but the total kinetic energy is not zero.

KE = +

     =

this means that the temperature of both substances will be equal