Question

an object that has a small mass and an object that has a small mass have the same momentum. which object has the largest kinetic energy?

Answer 1

Answer on Question #41962, Physics, Mechanics, Kinematics, Dynamics

An object that has a small mass and an object that has a large mass have the same momentum. Which object has the largest kinetic energy?

Solution:

The magnitude of each object's momentum is $p = m_1 v_1 = m_2 v_2$.

The kinetic energy of an object is

$$K = \frac{1}{2} m v^2 = \frac{1}{2} \frac{m \cdot m v^2}{m} = \frac{m^2 v^2}{2m} = \frac{p^2}{2m}$$

Thus, the object with the small mass has the largest kinetic energy.

**Answer.** the object with the small mass has the largest kinetic energy.

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