A 1.5 kg book on top a shelf has a PE of 29.4 J. How high is the shelf?
m g h = 29.4
1.5 * 9.81 * h = 29.4
solve for h
To calculate the height of the shelf, we can use the formula for potential energy:
PE = m * g * h
Where PE is the potential energy, m is the mass of the book, g is the acceleration due to gravity, and h is the height of the shelf.
Given:
m (mass of the book) = 1.5 kg
PE (potential energy) = 29.4 J
g (acceleration due to gravity) = 9.8 m/s^2
Substituting the values into the formula:
29.4 J = 1.5 kg * 9.8 m/s^2 * h
Simplifying the equation:
29.4 J = 14.7 N * h
Dividing both sides of the equation by 14.7 N:
h = 29.4 J / 14.7 N
h ≈ 2 meters
Therefore, the height of the shelf is approximately 2 meters.
To determine the height of the shelf, we can use the formula for gravitational potential energy:
PE = mgh
Where:
PE represents the potential energy (29.4 J)
m represents the mass of the book (1.5 kg)
g represents the acceleration due to gravity (approximately 9.8 m/s^2)
h represents the height of the shelf (unknown)
Rearranging the formula to solve for h:
h = PE / (mg)
Substituting the given values:
h = 29.4 J / (1.5 kg * 9.8 m/s^2)
Using a calculator:
h = 2 meters
Therefore, the height of the shelf is 2 meters.