A researcher is interested in determining the average length and weight of loblolly pine tree needles in the southeast United St
2 answers:
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Answer:
D) The objects velocity is zero when its acceleration is a maximum
Explanation:
In a simple harmonic motion, the total energy is constant (if we neglect air resistance and friction), and it is equal to the sum of the elastic potential energy U and the kinetic energy K:
(1)
where
m is the mass
v is the velocity
k is the spring constant
x is the displacement
As a consequence, since E must remain constant, when K increases U decreases, and vice-versa.
Also, in a simple harmonic motion the acceleration of the system is proportional to the negative of the displacement:
(2)
So, combining (1) with (2), we have the following situations:
- When the displacement is zero (x=0), the acceleration is also zero (a=0), and so the velocity is maximum, because the kinetic energy is maximum
- When the displacement is maximum (x=max), the acceleration is also maximum, while the velocity is zero because the kinetic energy is zero
So, the correct statement is
D) The objects velocity is zero when its acceleration is a maximum
First of all, we can find the mass of the person, since we know his weight W:
And so
We know for Newton's second law that the resultant of the forces acting on the person must be equal to the product between the mass and the acceleration a of the person itself:
There are only two forces acting on the person: his weight W (downward) and the vincular reaction Rv of the floor against the body (upward). So we can rewrite the previous equation as
We know the acceleration of the system,
(upward, so with same sign of Rv), so we can solve to find the value of Rv, the normal force exerted by the elevator's floor on the person:
And so
We know for Newton's second law that the resultant of the forces acting on the person must be equal to the product between the mass and the acceleration a of the person itself:
There are only two forces acting on the person: his weight W (downward) and the vincular reaction Rv of the floor against the body (upward). So we can rewrite the previous equation as
We know the acceleration of the system,