1). Distance is the length of the path he traveled. That's 3/4 of the circle.
Displacement is the length between where he started and where he ended.
That's 1/4 of the circle.
The circumference of a circle is (2 pi) · (the circle's radius) .
2). Force = (mass)·(acceleration) F = M·A
This is a very important formula. You should memorize it.
Whenever you see a problem that has force, mass, and
acceleration in it, this is the formula you need.
If you need to find acceleration (like in this problem),
divide each side by (mass), and then you have
Acceleration = (force) divided by (mass) .
First object: Mass=3, Force=5. Acceleration= 5/3 .
Second object: Mass=5, Force=3. Acceleration= 3/5 .
The question is asking for the ratio of these forces.
3). Guess what ! F = M · A .
Divide each side by Mass, and then you have
Acceleration = (force) divided by (mass)
= (80 N) / (50 kg) = ?
If the mass were doubled, it would be
(80 N) / (100 kg) = ?
4). The force of gravity changes opposite to the distance between
the objects. That's why the Earth pulls on us harder than Jupiter does.
The farther apart things are, the WEAKER gravity pulls them together.
How fast does the gravity force decrease ?
It decreases with the SQUARE of the distance.
That means . . .
-- If the distance changes to 3 times as far, the force becomes 1/3² = 1/9 .
-- If the distance changes to 2 times as far, the force becomes 1/2² = 1/4 .
-- If the distance changes to 1/3 as far, the force becomes (3²) = 9 .
-- If the distance changes to 1/2 as far, the force becomes (2²) = ?
5). A). The force of gravity increases as much as the PRODUCT of
the masses increases.
If one mass is B and the other mass is D, then the force calculation
has 'B·D' in it. If one of the masses doubles, then the calculation
has '2·B·D' in it. How much did the original force change ?
5). B). This was all covered in the discussion of #4).
6). 'Uniform velocity' means the object is moving in a straight line
with a constant speed. Its speed is not changing, and its direction
isn't changing either.
If a little tiny physicist is riding inside that object, there's NO TEST
he can do that can show him that he's moving. He has all of the SAME
laws of motion that any other physicist has, who's moving in any other
direction with any other constant speed.
7). Their masses are 'B' and 'D'. The original product is 'BD'.
When each mass is cut in half, they'll become B/2 and D/2.
Their product will become BD/4 .
That change alone will change the force to 1/4 of what it was originally.
If the distance between them is cut in half, then the force
changes to (2²) = 4 times what it was originally.
So the combined effect of all these changes at the same time
is that the new force is exactly equal to the original force.