The amount of potential energy, [tex]$P$[/tex], an object has is equal to the product of its mass, [tex]$m$[/tex], its height off the ground, [tex]$h$[/tex], and the gravitational constant, [tex]$g$[/tex]. This can be modeled by the equation [tex]$P=m g h$[/tex].
What is the equivalent equation solved for [tex]$h$[/tex]?
A. [tex]$\frac{\left(\frac{p}{m}\right)}{g}=h$[/tex]
B. [tex]$\frac{P}{m g}=h$[/tex]
C. [tex]$P m g=h$[/tex]
D. [tex]$\frac{P}{\left(\frac{m}{g}\right)}=h$[/tex]
Answer (1)
Start with the potential energy equation: P = m g h .
Divide both sides by m g to isolate h : m g P = m g m g h .
Simplify to find the equation for h : h = m g P .
The equivalent equation solved for h is m g P .
Explanation
Understanding the Problem We are given the equation for potential energy, P = m g h , where:
P is the potential energy,
m is the mass,
g is the gravitational constant,
h is the height off the ground.
Our goal is to solve this equation for h , which means we want to isolate h on one side of the equation.
Isolating h To isolate h , we need to divide both sides of the equation by m g . This gives us: m g P = m g m g h
Simplifying the right side, we get: m g P = h
Thus, the equation solved for h is: h = m g P
Final Answer Therefore, the equivalent equation solved for h is: h = m g P
Examples
Imagine you're designing a playground slide. You know the potential energy a child will have at the top ( P ) and the child's mass ( m ). Using the equation h = m g P , and knowing the gravitational constant g (approximately 9.8 m / s 2 ), you can calculate the necessary height ( h ) of the slide to ensure a safe and fun ride. This helps engineers design structures that are both safe and enjoyable for users.
