Which of the followning equations shows the relationship between the potential energy and height? Explain how you know.
potential energy=m(height)+b
potential energy=a(height)^2 +b(height)+c
potential energy=a/height
potential energy is a linear function of distance.
The equation that shows the relationship between potential energy and height is:
potential energy = m(height) + b
This equation represents a linear relationship between potential energy and height. The potential energy is calculated by multiplying the coefficient 'm' with the height, and then adding a constant term 'b'. Therefore, as the height increases, the potential energy will increase proportionally according to the coefficient 'm'. The constant term 'b' represents the potential energy at zero height, which can be thought of as the initial potential energy.
On the other hand, the equation potential energy = a(height)^2 + b(height) + c represents a quadratic relationship between potential energy and height. In this equation, the potential energy is calculated by multiplying the height squared by the coefficient 'a', adding the product of the height and coefficient 'b', and finally adding a constant term 'c'. This equation indicates that the potential energy is influenced by the square of the height, which means that as the height increases, the potential energy increases at an accelerating rate.
The equation potential energy = a/height, on the other hand, does not accurately represent the relationship between potential energy and height. In this equation, the potential energy is calculated by dividing the coefficient 'a' by the height. However, this equation does not align with the typical physics principles associated with potential energy and height.
In summary, the equation potential energy = m(height) + b represents the correct relationship between potential energy and height, based on the linear relationship between potential energy and height.