Question

Question #7b05d

Answer 1

Not enough information(?). See below.

Explanation:

I can think of a few different ways to go about this, but I don't think we (I) have enough information to provide the numerical answer they seem to be looking for...

One way that the force of gravity acting on an object can be described is by the product of the mass of the object and the gravitational acceleration constant, which differs from one body to another depending on its own mass. An object with a greater mass has a greater acceleration constant `g`. So, for example, we would expect `g_" Earth">g_" Moon"`, and indeed, this is the case.

`color(blue)(g_" Moon"~~1/6*g_" Earth"~~1.63" m"//"s"^2)`

We are actually given this information, as `"N"//"kg"="m"//"s"^2`. Though, again, this is the magnitude of the acceleration due to gravity, not a measure of the force of gravity.

It is important to note that mass and weight are two different quantities. The mass of an object does not change, regardless of where that object is located. You can think of mass as a measure of how much matter makes up an object. An object's weight on the other hand, depends on where that object is at a given time as well as the object's motion. The weight of an object depends on the acceleration that the object is experiencing, such as that due to gravity. We tend to think of weight on Earth as being equal to the force of gravity acting upon the object, as `F_(g"Earth")=mg_" Earth"`.

If the question is asking you specifically what your weight is on the moon, they want you to calculate your mass from your weight on Earth and use that to figure out your weight on the moon.

If the question is asking in general, what is your weight on the moon, we do not have enough numerical quantities to give a numerical answer by this method.

The best we could do is provide an equation.

Newton's Law of Gravitation

We could also use Newton's Law of Gravitation.

`color(blue)(F_G=G*(m_1xxm_2)/r)`

where:

• `F_G` is the force of gravitational attraction between the two bodies
• `G` is the universal gravitation constant `=6.67408xx10^-11m^3kg^-1s^-2`
• `m_1` and `m_2` are the masses of the two bodies experiencing gravitational attraction
• `r` is the radius, or distance, between the objects. For an object at the surface of the moon, this is the radius of the moon

`F_G` is still the weight you are looking for. However, you still need to know your mass or a general value for mass.