Calculate the work done by planet X on its moon.
Planet X applies a force of 5.6 x 10^10 N on its moon and the moon is 4.0 x 10^8 km away from the planet and it continues to circle the planet in a circular orbit of circumference of 2.5 x 10^9 m.
Well, well, seems like Planet X is quite the taskmaster! To calculate the work done by Planet X on its moon, we can use the formula:
Work = Force x Distance
Now, we have a couple of values to consider. The force applied by Planet X is 5.6 x 10^10 N, and the distance between the planet and the moon is 4.0 x 10^8 km.
However, we should convert that distance from kilometers to meters to keep things consistent. So, 4.0 x 10^8 km is equal to 4.0 x 10^11 m (since there are 1,000 meters in a kilometer).
Now, the formula for work becomes:
Work = (5.6 x 10^10 N) x (4.0 x 10^11 m)
Let's do the math, shall we?
Work = 2.24 x 10^22 Nm
So, the work done by Planet X on its moon is 2.24 x 10^22 Nm. That's quite the cosmic workout!
To calculate the work done by planet X on its moon, we need to determine the displacement and magnitude of the force.
Step 1: Convert the distance from km to meters:
4.0 x 10^8 km = 4.0 x 10^8 * 10^3 m = 4.0 x 10^11 m
Step 2: Calculate the displacement of the moon.
In a circular orbit, the displacement is equal to the circumference of the orbit, which is given as 2.5 x 10^9 m.
Step 3: Calculate the work done.
The work done (W) is given by the equation:
W = F * d * cosθ
Where:
W = work done
F = force applied
d = displacement
θ = angle between the force vector and the displacement vector (in this case, θ is 0 degrees, because the force and displacement vectors are in the same direction)
Substituting the given values:
W = (5.6 x 10^10 N) * (2.5 x 10^9 m) * cos(0)
Since cos(0) is equal to 1, the equation simplifies to:
W = (5.6 x 10^10 N) * (2.5 x 10^9 m)
Multiplying these values:
W = 1.4 x 10^20 N * m
Therefore, the work done by planet X on its moon is 1.4 x 10^20 N * m.
To calculate the work done by planet X on its moon, we can use the formula:
Work = Force * Distance * cos(angle)
In this case, the force applied by planet X on its moon is 5.6 x 10^10 N. The distance between the planet and its moon is given as 4.0 x 10^8 km. However, it is more convenient to work with meters, so we need to convert the distance to meters by multiplying by 1000:
Distance = 4.0 x 10^8 km * 1000 = 4.0 x 10^11 m
Now, let's find the angle between the force applied by the planet and the displacement of the moon. Since the moon is in a circular orbit, the angle between the force and displacement is 0 degrees, and cos(0) is equal to 1.
Therefore, the formula becomes:
Work = 5.6 x 10^10 N * 4.0 x 10^11 m * cos(0)
Since cos(0) is equal to 1, the formula simplifies to:
Work = 5.6 x 10^10 N * 4.0 x 10^11 m
Now we can multiply the numbers:
Work = 22.4 x 10^21 N * m
To make the answer more readable, we can write it in scientific notation:
Work = 2.24 x 10^22 N * m
So, the work done by planet X on its moon is 2.24 x 10^22 N * m.