Answer:
C) 1 s
Explanation:
The period of a mass-spring system is given by the formula:
where
m is the mass hanging on the spring
k is the spring constant
As we can see from the equation above, the period of the system does NOT depend on the initial amplitude of the oscillation. Therefore, even if the initial amplitude is changed from 5 cm to 10 cm, the period of the system will remain the same, 1 s.
a)
b) 5843 N
Explanation:
a)
The position of the UFO at time t is given by the vector:
Therefore it has 3 components:
We start by finding the velocity of the UFO, which is given by the derivative of the position:
And then, by differentiating again, we find the acceleration:
The weight of the UFO is W = 12,500 N, so its mass is:
Therefore, the components of the force on the UFO are given by Newton's second law:
So, Substituting t = 2 s, we find:
So the net force on the UFO at t = 2 s is
b)
The magnitude of a 3-dimensional vector is given by
where
are the three components of the vector
In this problem, the three components of the net force are:
Therefore, substituting into the equation, we find the magnitude of the net force:
Answer:
Explanation:
This is a simple gravitational force problem using the equation:
where F is the gravitational force, G is the universal gravitational constant, the m's are the masses of the2 objects, and r is the distance between the centers of the masses. I am going to state G to 3 sig fig's so that is the number of sig fig's we will have in our answer. If we are solving for the gravitational force, we can fill in everything else where it goes. Keep in mind that I am NOT rounding until the very end, even when I show some simplification before the final answer.
Filling in:
I'm going to do the math on the top and then on the bottom and divide at the end.
and now when I divide I will express my answer to the correct number of sig dig's:
6.45 × 10¹⁶ N