A 3.60 kg book is initially on a shelf located 1.80 m above the floor. The book is moved from the shelf to a coffee table that is just 0.380 m above the floor. What is the change in the book’s gravitational potential energy?
Change = m*g*h1 - m*g*h2
Change=(3.6*9.8*1.8) - 3.6*9.8*0.380 =
63.50 - 13.4 = 50.1 J.
To find the change in the book's gravitational potential energy, we need to calculate the difference in potential energy between its initial and final positions.
The gravitational potential energy (PE) of an object is given by the equation:
PE = mgh
Where:
m = mass of the object
g = acceleration due to gravity
h = height or distance above a reference point
Given:
Mass of the book (m) = 3.60 kg
Initial height (h1) = 1.80 m
Final height (h2) = 0.380 m
First, we calculate the initial potential energy (PE1) when the book is on the shelf:
PE1 = m * g * h1
Second, we calculate the final potential energy (PE2) when the book is on the coffee table:
PE2 = m * g * h2
Finally, we find the change in the book's gravitational potential energy (ΔPE) by subtracting the initial potential energy from the final potential energy:
ΔPE = PE2 - PE1
Let's plug in the given values and calculate:
PE1 = 3.60 kg * 9.8 m/s² * 1.80 m
PE1 = 63.504 J
PE2 = 3.60 kg * 9.8 m/s² * 0.380 m
PE2 = 13.5056 J
ΔPE = PE2 - PE1
ΔPE = 13.5056 J - 63.504 J
ΔPE = -49.9984 J
Therefore, the change in the book's gravitational potential energy is approximately -49.9984 J.