A book that weighs 0.35 kilograms is kept on a shelf that’s 2.0 meters above the ground. A picture frame that weighs 0.5 kilograms will have the same gravitational potential energy as the book when it’s raised to a height of
meters.
To find the height at which the picture frame will have the same gravitational potential energy as the book, we can use the formula for gravitational potential energy:
Potential Energy = mass * gravitational acceleration * height
The mass of the book is given as 0.35 kilograms. The weight of an object is given by the formula:
Weight = mass * gravitational acceleration
Since the gravitational acceleration is a constant, we can express the weight of the book as:
Weight of book = mass of book * gravitational acceleration
However, in this case, the weight of the book is not given. We can calculate it using the formula:
Weight = mass * gravitational acceleration
Given that the weight of the book is equal to the weight of the picture frame, we have:
Weight of book = Weight of picture frame
Now we can solve for the height of the picture frame:
mass of book * gravitational acceleration * height of book = mass of picture frame * gravitational acceleration * height of picture frame
Since the mass of the book is given as 0.35 kilograms, the weight of the book can be calculated as:
Weight of book = 0.35 kilograms * gravitational acceleration
Similarly, the weight of the picture frame can be calculated as:
Weight of picture frame = 0.5 kilograms * gravitational acceleration
Now we can set up the equation:
0.35 kilograms * gravitational acceleration * height of book = 0.5 kilograms * gravitational acceleration * height of picture frame
Simplifying the equation, we can cancel out the gravitational acceleration on both sides:
0.35 kilograms * height of book = 0.5 kilograms * height of picture frame
Now we can solve for the height of the picture frame:
height of picture frame = (0.35 kilograms * height of book) / 0.5 kilograms
Plug in the given value for the height of the book (2.0 meters):
height of picture frame = (0.35 kilograms * 2.0 meters) / 0.5 kilograms
Simplifying the equation, we get:
height of picture frame = 0.7 meters
Therefore, the picture frame will have the same gravitational potential energy as the book when it is raised to a height of 0.7 meters.
To determine the height at which the picture frame will have the same gravitational potential energy as the book, we can use the equation:
Gravitational potential energy = (mass) x (acceleration due to gravity) x (height)
Let's denote the height as "h".
For the book:
Gravitational potential energy of the book = (0.35 kg) x (9.8 m/s^2) x (2.0 m) = 6.86 Joules
Setting the gravitational potential energy of the picture frame equal to the book's potential energy and solving for "h":
(0.5 kg) x (9.8 m/s^2) x (h) = 6.86 Joules
0.5h = 6.86 Joules / (9.8 m/s^2)
h = (6.86 Joules / (9.8 m/s^2)) / 0.5 kg
Using a calculator, we find:
h ≈ 1.41 meters
Therefore, when the picture frame is raised to a height of approximately 1.41 meters, it will have the same gravitational potential energy as the book.
just match the values:
0.5h = 0.35 * 2.0