KE, GPE & EPE

• Definition: Kinetic energy is the energy an object possesses due to its motion. Any object with mass that is moving at a specific velocity has a kinetic energy store.

• Mathematical Relationship: The amount of kinetic energy is directly proportional to the mass of the object and the square of its speed. This means doubling the speed of an object will quadruple its kinetic energy.

Formula: $E_k = \frac{1}{2}mv^2$

• $m$: mass ($kg$)
• $v$: speed ($m/s$)

• Definition: GPE is the energy stored in an object due to its vertical position (height) within a gravitational field. Work must be done against gravity to lift an object, which is then stored as GPE.

• Field Strength: On Earth, the gravitational field strength ($g$) is approximately $9.8$ or $10$ $N/kg$. The GPE depends on the mass, the strength of this field, and the change in height.

Formula: $\Delta E_p = mgh$

• $m$: mass ($kg$)
• $g$: gravitational field strength ($N/kg$)
• $h$: change in height ($m$)

• Definition: EPE is the energy stored in an object when it is temporarily deformed, such as being stretched or compressed. This applies to objects like springs or elastic bands.

• Spring Constant ($k$): This value represents the stiffness of the object. A higher spring constant means more force is required to stretch the object by a certain distance.

• Extension ($x$): The energy stored increases with the square of the extension (or compression) from the equilibrium position.

Formula: $E_e = \frac{1}{2}kx^2$

• $k$: spring constant ($N/m$)
• $x$: extension or compression ($m$)

• Velocity vs. Height: While GPE increases linearly with height, KE increases exponentially with speed. This is why high-speed collisions are significantly more energetic than low-speed ones.

• Unit Conversion: Always check if mass is in grams ($g$) and convert to kilograms ($kg$) by dividing by $1000$. Similarly, convert centimeters ($cm$) to meters ($m$) for height and extension.

• Conservation Principle: In many exam problems, you will need to equate one energy store to another (e.g., $GPE_{top} = KE_{bottom}$). This assumes no energy is lost to the surroundings as heat or sound.

• Rearranging Formulas: Practice isolating variables. For example, to find velocity from KE, use $v = \sqrt{\frac{2E_k}{m}}$. Forgetting the square root is a very common error.

• Reference Levels: For GPE, always define where $h=0$ is (usually the lowest point in the problem) to keep calculations consistent.