Answer:
Both forces are the same.
Explanation:
The problem states that:
The force exerted on the moon by earth is given by:
where K is the gravitational constant, and d is the separation distance between the earth and the moon.
The force exerted on the earth by moon is given by:
where K is the gravitational constant, and d is the separation distance between the earth and the moon.
The relation is therefore:
As you can see, they are the same.
Explanation:
It is given that net gravitational force on M is exactly equal to zero. Hence, distance to M from the bigger mass is 3m. Therefore, expression for net force will be as follows.
So,
The first term is negative as the third mass is located between the other two masses. This means that 3 m will be pulling it leftwards (negative x direction) and m will be pulling it rightwards (positive x direction).
On dividing both sides of the equation by G.m.M, we get the following.
0 =
Using the formula, the value of x comes out to be equal to +2.37 (not usabale) and -0.634 (usable).
Hence, we can conclude that the third mass will be located 0.634 meters away from the 3 m mass.
Answer:
The cannon has an initial speed of 13.25 m/s.
Explanation:
The launched cannonball is an example of a projectile. Thus, its launch speed can be determined by the application of the formula;
R = u
Where: R is the range of the projectile, u is its initial speed, H is the height of the cliff and g is the gravitaty.
R = 26.3 m, H = 19.3 m, g = 9.8 m/.
So that:
26.3 = u
=
x
691.69 = x
=
=
= 175.6104
⇒ u =
= 13.2518
u = 13.25 m/s
The initial speed of the cannon is 13.25 m/s.