Final answer:
To solve for height (h) in the G.P.E. formula E = mgh, divide the gravitational potential energy (E) by the product of mass (m) and gravity (g), resulting in h = E / (mg). Then substitute the known values for E, m, and g to find h in meters.
Step-by-step explanation:
To solve for the height (h) in the gravitational potential energy formula E = mgh, we want to isolate h. The formula for gravitational potential energy (G.P.E.) is dependent on mass (m), gravitational acceleration (g), and height (h). Given that the gravitational potential energy (E) is known, we can rearrange the formula to solve for h by dividing both sides of the equation by the product of mass and gravitational acceleration.
Step-by-Step Solution
- Start with the formula E = mgh.
- Divide both sides by mg to isolate h: h = E / (mg).
- Plug in the values for E (energy in Joules), m (mass in kilogram), and g (acceleration due to gravity, approximately 9.8 m/s² or rounded to 10 m/s² for simpler calculations).
- Solve for h, which will give you the height in meters.
If, for example, the gravitational potential energy E of an object is known to be 100 Joules, and its mass m is 2 kilograms, using the approximate value for g of 10 m/s², the height h would be calculated as follows:
h = E / (mg) = 100 / (2×10) = 100 / 20 = 5 meters.