A woman runs up a flight of stairs. The gain in her gravitational potential energy is 6500 J. If she runs up the stairs at half the speed, what is her gain in gravitational potential energy?
lol same cause Ep=mgh
mass gravity height havent changed
6500 J
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To determine the gain in gravitational potential energy if the woman runs up the stairs at half the speed, we need to understand the relationship between gravitational potential energy and speed.
Gravitational potential energy (PE) is given by the formula:
PE = mgh
Where:
m = mass of the object (in this case, the woman)
g = acceleration due to gravity (approximately 9.8 m/s²)
h = height or altitude gain
In this case, the mass of the woman cancels out, as we are interested in the change in gravitational potential energy, not the actual value. Therefore, we can ignore the mass.
Given that her gain in gravitational potential energy is 6500 J, we can solve for the height (h) by rearranging the formula:
h = PE / (mg)
Since we know the gain in potential energy (PE) and the acceleration due to gravity (g), we can substitute the values to find the height.
Now let's calculate the height:
h = 6500 J / (9.8 m/s²)
h = 663.27 meters
Now, to determine the new gain in gravitational potential energy when the woman runs at half the speed, we need to use the new height value and the same formula:
PE = mgh
Since the height (h) is halved, we can substitute the new height value and solve for the new potential energy.
Let's calculate the new gain in gravitational potential energy:
PE = mgh (new)
PE = m * (h / 2) * g
PE = (mgh) / 2
Substituting the known values:
PE (new) = (6500 J) / 2
PE (new) = 3250 J
Therefore, when the woman runs up the stairs at half the speed, her gain in gravitational potential energy is 3250 J.