True or False: Kinetic energy is a vector quantity with magnitude and direction. True False Only the component of force parallel to the displacement does work. True False A ball is thrown upward into the air. As the ball rises and slows, the kinetic energy increases and the gravitational potential energy decreases. True False
The Correct Answer and Explanation is:
Here are the correct answers:
- Kinetic energy is a vector quantity with magnitude and direction. — False
- Only the component of force parallel to the displacement does work. — True
- A ball is thrown upward into the air. As the ball rises and slows, the kinetic energy increases and the gravitational potential energy decreases. — False
Understanding the principles of energy and motion in physics requires careful attention to definitions and the relationships between physical quantities.
1. Kinetic Energy as a Scalar:
Kinetic energy is defined as $KE = \frac{1}{2}mv^2$, where $m$ is mass and $v$ is speed (the magnitude of velocity). Although velocity is a vector, kinetic energy depends only on its magnitude (speed), not its direction. Therefore, kinetic energy is a scalar quantity, not a vector—it has magnitude but no direction. This is why the first statement is false.
2. Work Done by Force Components:
Work is defined as $W = \vec{F} \cdot \vec{d} = Fd\cos\theta$, where $\vec{F}$ is force, $\vec{d}$ is displacement, and $\theta$ is the angle between them. This equation shows that only the component of force in the direction of the displacement (parallel component) contributes to work. Perpendicular force components (e.g., centripetal force in circular motion) do no work. Therefore, the second statement is true.
3. Energy of a Rising Ball:
When a ball is thrown upward, it slows down due to gravity. As it rises, kinetic energy decreases because its speed decreases. At the same time, its gravitational potential energy increases because it gains height. So the third statement, which claims that kinetic energy increases and potential energy decreases, is false—it’s actually the opposite.
In summary, kinetic energy is a scalar, only force parallel to displacement does work, and a rising object loses kinetic energy while gaining potential energy. Understanding these fundamentals helps in analyzing a wide range of motion and energy scenarios in physics.
