Question

1. what is the formula for gravitational potential energy?
2. what is the formula for kinetic energy?
3. how does mass affect kinetic energy?
4. how does velocity affect kinetic energy?

Explanation:

Step1: Gravitational potential energy formula

The formula for gravitational potential energy near the Earth's surface is $U = mgh$, where $m$ is the mass of the object, $g$ is the acceleration due to gravity ($g\approx9.8\ m/s^{2}$ on Earth's surface), and $h$ is the height of the object above a reference - level.

Step2: Kinetic energy formula

The formula for kinetic energy is $K=\frac{1}{2}mv^{2}$, where $m$ is the mass of the object and $v$ is its velocity.

Step3: Mass - kinetic energy relationship

From the kinetic - energy formula $K = \frac{1}{2}mv^{2}$, when the velocity $v$ is constant, the kinetic energy $K$ is directly proportional to the mass $m$. That is, if the mass of an object increases, its kinetic energy increases, and if the mass decreases, its kinetic energy decreases.

Step4: Velocity - kinetic energy relationship

From the kinetic - energy formula $K=\frac{1}{2}mv^{2}$, when the mass $m$ is constant, the kinetic energy $K$ is directly proportional to the square of the velocity $v$. So, a small change in velocity can cause a large change in kinetic energy. For example, if the velocity of an object doubles, its kinetic energy quadruples ($K'=\frac{1}{2}m(2v)^{2}=4\times\frac{1}{2}mv^{2} = 4K$).

Answer:

1. $U = mgh$
2. $K=\frac{1}{2}mv^{2}$
3. When velocity is constant, kinetic energy is directly proportional to mass.
4. When mass is constant, kinetic energy is directly proportional to the square of the velocity.