A Triangle of Equal Gravitational Forces?

[dhphysics]

I have 3 questions. I think the answers are correct, but I'm having trouble providing explanations.

Homework Statement

Three particles have identical masses. Each particle experiences only the gravitational forces due to the other two particles. How should the particles be arranged so each one experiences a net gravitational force that has the same magnitude?
. The attempt at a solution
- I think you would put them at the corners of a equilateral triangle, because then they would be equidistant from each other, so their net gravitational forces are the same. Is this correct logic?

Homework Statement

A 10-kg suitcase is placed on a scale that is in an elevator. Is the elevator accelerating up or down when the scale reads the following?

... 75 N?
. The attempt at a solution
The elevator is going down. I'm not sure how to come up with a correct reason; it is intuitive.

...120 N?
. The attempt at a solution
The elevator is going up. Again, how would I justify this in physics terms?

Homework Statement

A person has a choice of either pushing or pulling a sled at a constant velocity. Friction is present. Does it require less force to push or to pull?
[FONT=verdana, helvetica, sans-serif]. The attempt at a solution
Pulling requires less force because if you pull, then you apply an upwards force and so friction is reduced, making the horizontal component of the force not needing to be as big.

 

[Simon Bridge]

1. Force is a vector. You are correct about the magnitude - and that will be all the question really wants.
The directions will also be the same in the sense that they are all radially towards the center of the triangle.

2&3. Intuition can be a good clue - you should try to figure where your intuition comes from: when the elevator accelerates down, with you in it, do you feel lighter or heavier?

Notice that the question is careful to talk about the acceleration, rather than just which direction it is "going"?
Why do they do that?

When the elevator accelerates up - it presses the scales against the bottom of the case more than just enough to cancel gravity ... the scales measure how hard the elevator presses against the case. If the elevator accelerated down with acceleration greater than 9.8m/s, what would the scales read?

4. If you pull the sled by it's rope/handle then you automatically combine lifting with pulling.
Like with 1, this is probably the answer they are looking for.

 

[charl1e]

So, for your first problem, Newton's Law for Gravitation between two objects has the variables: the mass of the first particle, the mass of the second particle, and the magnitude of the distance between the two particles (since in this problem, we're focusing on just the magnitude of the gravitational force). Since the masses of all the individual particles are the same, the only way we can vary the magnitude of the gravitational force is by varying the distance between the two particles in question. Now, all we need to do is to find a 'shape'/orientation such that it has the number of vertices that match how many particles there are (in this case 3), so we need a triangle. We also need a shape in which the distance between each vertex is equal. As you said, an equilateral triangle is perfect for this!

It's very intuitive (the second and third question), since most of us have been in elevators and we've felt heavier or lighter depending on which way the elevator is accelerating (upwards or downwards, sadly they haven't made elevators that travel in any other direction yet - from my current knowledge). The scale reads the amount of force that is being applied to it (from the suitcase). The suitcase always has the gravitational force due to the Earth acting on it. While the elevator is stationary (relative to the suitcase) there is a force acting on the scales due to this suitcase (F = ma = (mass of suitcase)(gravitational acceleration due to earth)). Now let's suppose the elevator accelerates downwards relative to the suitcase, but let's change it up a bit so it's much easier to visualize and understand. Let us be the elevator. So, relative to us (the elevator) - being stationary - the suitcase accelerates downwards a bit less than normal (the human is accelerating upwards, still with the constant acceleration downwards due to the gravitational effects of the Earth - this being all relative to the elevator). Therefore the suitcase applies less force to the scale (the suitcase is not accelerating downwards as fast as normal). This goes for the third question, but the other way around. The suitcase accelerates faster towards the scales than normal!

Hope that helps,

Charlie