An object on the moon will weigh 1/6th of what it does on earth but have the same mass. Why is that?

Because the weight depends of the gravity

Explanation:

This is because weight and mass are different, in order to better understand this problem we will apply an example with real values, which will help us to determine a person's weight.

A man has a mass of 80 [kg] on Earth when measuring his weight he realizes that it is 784.9 [N] and on the moon it is 130.8 [N]

On Earth

Where:

g = gravity

Weight on the moon

Wm = 80 * 1.635

Wm = 130.8[N]

Weight on the earth

We = 80 * 9.81

We = 784.8[N]

In this way we can see that the weight depends on the gravity of where the person is located.

v=ir = 3x15 =45 v