Mary weighs 510 N. She walks down a flight of stairs to a level 5.65 m below her starting point. What is the change in Mary's potential energy? Assume that air resistance is negligible.
Question
Mary weighs 510 N. She walks down a flight of stairs to a level 5.65 m below her starting point. What is the change in Mary's potential energy? Assume that air resistance is negligible.
Solution
To calculate the change in potential energy, we can use the formula:
Potential Energy (PE) = mass * gravity * height
However, we are given the weight of Mary, not her mass. We know that weight = mass * gravity. So, we can find the mass first.
Given: Weight (W) = 510 N Gravity (g) = 9.8 m/s² (approximate value on Earth)
We can rearrange the weight formula to find mass:
Mass (m) = Weight / Gravity m = 510 N / 9.8 m/s² m ≈ 52.04 kg
Now we can calculate the change in potential energy. The height (h) is 5.65 m.
Change in PE = m * g * h Change in PE = 52.04 kg * 9.8 m/s² * 5.65 m Change in PE ≈ 2876.57 Joules
So, the change in Mary's potential energy as she walks down the stairs is approximately 2876.57 Joules.
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