A classmate throws a 1.1-kg book from a height of 1.3 m above the ground straight up into the air. The book reaches a maximum height of 4.0 m above the ground and begins to fall back. Assume that 1.3 m above the ground is the reference level for zero gravitational potential energy.
Determine the gravitational potential energy of the book when it hits the ground.
then it is GPE=mgh=-mg*1.3
To determine the gravitational potential energy of the book when it hits the ground, we can use the equation:
Gravitational Potential Energy = m * g * h
Where:
m = mass of the book (1.1 kg)
g = acceleration due to gravity (9.8 m/s², assuming Earth's gravity)
h = height above the reference level (1.3 m)
First, we need to calculate the gravitational potential energy at the maximum height of 4.0 m. Using the same equation:
Gravitational Potential Energy = m * g * h
m = 1.1 kg
g = 9.8 m/s²
h = 4.0 m
Gravitational Potential Energy at maximum height = 1.1 kg * 9.8 m/s² * 4.0 m
Now, to find the gravitational potential energy when the book hits the ground, we need to subtract the initial height of 1.3 m from the maximum height (4.0 m):
Height above the reference level when it hits the ground = maximum height - initial height
Height above the reference level when the book hits the ground = 4.0 m - 1.3 m
Now we can calculate the gravitational potential energy when the book hits the ground:
Gravitational Potential Energy when it hits the ground = m * g * (Maximum height - Initial height)
Gravitational Potential Energy = 1.1 kg * 9.8 m/s² * (4.0 m - 1.3 m)
Finally, evaluate the equation to find the answer:
Gravitational Potential Energy = 1.1 kg * 9.8 m/s² * 2.7 m
Therefore, the gravitational potential energy of the book when it hits the ground is 28.35 J (Joules).