Mary weighs 485 N. She walks down a flight of stairs to a level 5.55 m below her starting point. What is the change in Mary's potential energy? Assume that air resistance is negligible.
The change in Mary's potential energy can be calculated using the formula:
ΔPE = m * g * h
Where:
ΔPE is the change in potential energy
m is the mass (weight) of the object
g is the acceleration due to gravity (approximately 9.8 m/s²)
h is the height or change in height
Given:
Mary's weight (m) = 485 N
Change in height (h) = -5.55 m (negative because she is descending)
Using the formula, we can calculate the change in Mary's potential energy:
ΔPE = 485 N * 9.8 m/s² * -5.55 m
ΔPE ≈ -26,727.3 J
Therefore, the change in Mary's potential energy is approximately -26,727.3 J.
To find the change in Mary's potential energy, we need to first determine her initial potential energy and her final potential energy.
The potential energy of an object near the Earth's surface can be calculated using the formula:
PE = m * g * h
Where:
PE is the potential energy,
m is the mass of the object,
g is the acceleration due to gravity (approximately 9.8 m/s^2), and
h is the height or vertical displacement.
Given that Mary's weight is 485 N, we can calculate her mass using the formula:
Weight = m * g
Rearranging the equation to solve for mass:
m = Weight / g
Substituting the given values:
m = 485 N / 9.8 m/s^2 = 49.49 kg (approximately)
Now we can calculate her initial potential energy:
PE_initial = m * g * h_initial
Since she starts at ground level, her initial height (h_initial) is 0.
PE_initial = 49.49 kg * 9.8 m/s^2 * 0 = 0 J (Joules)
Next, we calculate her final potential energy:
PE_final = m * g * h_final
Given that she walks down a flight of stairs to a level 5.55 m below her starting point, her final height (h_final) is -5.55 m (negative since she has descended).
PE_final = 49.49 kg * 9.8 m/s^2 * (-5.55 m) = -2,722.97 J (Joules)
Thus, the change in Mary's potential energy is:
Change in PE = PE_final - PE_initial
= -2,722.97 J - 0 J
= -2,722.97 J
The negative sign indicates that her potential energy has decreased on descending the stairs.
mg = 485 N.
PE = mgh = 485 * 5.55 = 2692 Joules.