if the separation distance between the moon and the planet is increased by a factor of 4 then the force gravitational is
2 answers:
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Answer:
Time period of horizontal Oscillation = T = 2
As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.
Explanation:
Solution:
As we know that:
F = Kx
Here,
K = Spring constant
x = displacement.
First, they are displacing it with 6 cm from its rest position for which Time period of the oscillation is T = 2 seconds.
But next, they want to know the effect on the time period of the oscillation if the displacement x is doubled from 6cm to 12 cm.
First of all, let us see the equation of the time period of the oscillation.
We need to check, if time period does depend on the displacement or not.
As we know,
Time period of horizontal Oscillation = T = 2
As you can see, from the equation, Period of oscillation depends upon the mass and the spring constant. Not on the displacement.
Since, K is the constant for a particular spring, we need to change the mass of the cart to change the time period.
Hence the Time period will remain same.
To solve this problem we will apply the linear motion kinematic equations. From the definition of the final velocity, as the sum between the initial velocity and the product between the acceleration (gravity) by time, we will find the final velocity. From the second law of kinematics, we will find the vertical position traveled.
Here,
v = Final velocity
= Initial velocity
g = Acceleration due to gravity
t = Time
At t = 4s, v = -30m/s (Downward)
Therefore the initial velocity will be
Now the position can be calculated as,
When it has the ground, y=0 and the time is t=4s,
Therefore the cliff was initially to 41.6m from the ground