You have a 120g yoyo that you are swinging at 0.9m/s. How much energy does it have? How high can it get above the lowest point of the swing without your doing any additional work, or Earth? How high could it get on the Moon, where gravity is 1/6 Earth's?
To calculate the energy of the yoyo, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the mass of the yoyo is 120g (or 0.12 kg) and the velocity is 0.9 m/s, we can substitute these values into the formula:
Kinetic Energy = (1/2) * 0.12 kg * (0.9 m/s)^2
= (1/2) * 0.12 kg * 0.81 m^2/s^2
= 0.049 J
Therefore, the yoyo has approximately 0.049 Joules of energy.
To determine how high the yoyo can reach above the lowest point of the swing without any additional work or Earth's influence, we can equate the potential energy at that height to the kinetic energy of the yoyo at its maximum velocity.
Potential Energy = Kinetic Energy
The formula for potential energy is:
Potential Energy = mass * gravity * height
Since the mass of the yoyo is 0.12 kg and the acceleration due to gravity on Earth is approximately 9.8 m/s^2, we can rearrange the equation to solve for height:
height = Kinetic Energy / (mass * gravity)
height = 0.049 J / (0.12 kg * 9.8 m/s^2)
= 0.042 m
Therefore, the yoyo can reach a height of approximately 0.042 meters (or 4.2 centimeters) above the lowest point of the swing without additional work or Earth's influence.
Now, to calculate the maximum height the yoyo could reach on the Moon, where gravity is 1/6th of Earth's gravity, we need to consider the modified acceleration due to gravity.
The acceleration due to gravity on the Moon is 1/6 * 9.8 m/s^2 = 1.633 m/s^2.
Using the same formula, we can calculate the height:
height (on Moon) = Kinetic Energy / (mass * gravity (on Moon))
= 0.049 J / (0.12 kg * 1.633 m/s^2)
= 0.249 m
Therefore, the yoyo could reach a maximum height of approximately 0.249 meters (or 24.9 centimeters) on the Moon.