Antwan raised a 11.0 N physics book from a table 75 cm above the floor to a shelf 2.45 m above the floor. What was the change in the potential energy of the system?
Question
Antwan raised a 11.0 N physics book from a table 75 cm above the floor to a shelf 2.45 m above the floor. What was the change in the potential energy of the system?
Solution
The change in potential energy can be calculated using the formula:
ΔPE = m * g * Δh
where:
- ΔPE is the change in potential energy,
- m is the mass of the object,
- g is the acceleration due to gravity, and
- Δh is the change in height.
First, we need to find the mass of the book. We know that the weight of the book is 11.0 N and weight is the product of mass and gravity. So, we can find the mass as follows:
m = W / g m = 11.0 N / 9.8 m/s² m ≈ 1.12 kg
Next, we need to find the change in height. The book was moved from a table 75 cm above the floor to a shelf 2.45 m above the floor. We need to convert the height from cm to m:
75 cm = 0.75 m
So, the change in height is:
Δh = h_final - h_initial Δh = 2.45 m - 0.75 m Δh = 1.7 m
Finally, we can find the change in potential energy:
ΔPE = m * g * Δh ΔPE = 1.12 kg * 9.8 m/s² * 1.7 m ΔPE ≈ 18.6 J
So, the change in the potential energy of the system was approximately 18.6 Joules.
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