The effective spring constant of the system is 39.6 N/m
Explanation:
The frequency of oscillation of a spring-mass system is given by
where
k is the spring constant of the system
m is the mass
In this problem, we have:
f = 29 Hz is the frequency of vibration of the eyeball system
m = 7.5 g = 0.0075 kg is the mass
We can therefore re-arrange the equation to find the effective spring constant of the system. We find:
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Answer:
a) It is moving at when reaches the ground.
b) It is moving at when reaches the ground.
Explanation:
Work energy theorem states that the total work on a body is equal its change in kinetic energy, this is:
(1)
with W the total work, Ki the initial kinetic energy and Kf the final kinetic energy. Kinetic energy is defined as:
(2)
with m the mass and v the velocity.
Using (2) on (1):
(3)
In both cases the total work while the objects are in the air is the work gravity field does on them. Work is force times the displacement, so in our case is weight (w=mg) of the object times displacement (d):
(4)
Using (4) on (3):
(5)
That's the equation we're going to use on a) and b).
a) Because the branch started form rest initial velocity (vi) is equal zero, using this and solving (5) for final velocity:
b) In this case the final velocity of the boulder is instantly zero when it reaches its maximum height, another important thing to note is that in this case work is negative because weight is opposing boulder movement, so we should use -mgd:
Solving for initial velocity (when the boulder left the volcano):