A 3.47 kg ball is attached to a ceiling by a 1.63 m long string. The height of the room is 5.59 m. What is the gravitational potential energy of the ball relative to the ceiling?
gpe= mg*(-1.63)
To calculate the gravitational potential energy of the ball relative to the ceiling, we need to use the formula:
Potential Energy = mass × gravity × height
First, let's gather the given information:
Mass of the ball (m) = 3.47 kg
Length of the string (l) = 1.63 m
Height of the room (h) = 5.59 m
Acceleration due to gravity (g) = 9.8 m/s^2 (approximately)
Now, we need to determine the vertical distance traveled by the ball from its initial position (attached to the ceiling) to its final position (at the given height):
Vertical distance = height - length of the string
= 5.59 m - 1.63 m
= 3.96 m
Next, we can calculate the gravitational potential energy by substituting the values into the formula:
Potential Energy = mass × gravity × height
= 3.47 kg × 9.8 m/s^2 × 3.96 m
≈ 135.114 J
Therefore, the gravitational potential energy of the ball relative to the ceiling is approximately 135.114 J.