To solve these problems, we can use the formula for gravitational potential energy (GPE), which is given by:
GPE = mass * gravitational acceleration * height
The gravitational acceleration on Earth is approximately 9.8 m/s².
Now let's solve these problems one by one using the formula above:
**Problem 1:**
A football player throws a ball with a mass of 0.34 kg. What is the gravitational potential energy of the ball when it is 5.0 m above the ground?
- The mass of the ball (m) = 0.34 kg
- The height above the ground (h) = 5.0 m
- Gravitational acceleration (g) = 9.8 m/s²
Now we calculate the GPE:
GPE = m * g * h
GPE = 0.34 kg * 9.8 m/s² * 5.0 m
GPE = 1.692 kg*m²/s² * 5
GPE = 8.46 kg*m²/s²
Therefore, the gravitational potential energy of the ball when it is 5.0 m above the ground is 8.46 Joules.
**Problem 2:**
A 2.0-kg book is on a shelf that is 1.6 m high. What is the gravitational potential energy of the book relative to the ground?
- The mass of the book (m) = 2.0 kg
- The height of the shelf (h) = 1.6 m
Using the same formula:
GPE = m * g * h
GPE = 2.0 kg * 9.8 m/s² * 1.6 m
GPE = 19.6 kg*m²/s² * 1.6
GPE = 31.36 kg*m²/s²
Therefore, the gravitational potential energy of the book is 31.36 Joules relative to the ground.
**Problem 3:**
A 36-kg girl walks to the top of stairs that are 2.0-m high. How much gravitational potential energy does the girl gain?
- The mass of the girl (m) = 36 kg
- The height of the stairs (h) = 2.0 m
Again, using the formula:
GPE = m * g * h
GPE = 36 kg * 9.8 m/s² * 2.0 m
GPE = 352.8 kg*m²/s² * 2
GPE = 705.6 kg*m²/s²
Thus, the girl gains 705.6 Joules of gravitational potential energy by walking to the top of the 2.0-m high stairs.
