A roller coaster, traveling with an initial speed of 15 meters per second, decelerates uniformly at –7.0 m/s2 to a full stop. Ap
1 answer:
Answer:
Roller coaster will travel 16.07 meter before coming to stop.
Explanation:
We have equation of motion, , where u is the initial velocity, u is the final velocity, s is the displacement and a is the acceleration.
In this case we have final velocity = 0 m/s, initial velocity = 15 m/s, and acceleration = -7 .
So, roller coaster will travel 16.07 meter before coming to stop.
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A)
The total energy of the system is equal to the maximum elastic potential energy, that is achieved when the displacement is equal to the amplitude (x=A):
(1)
where k is the spring constant.
The total energy, which is conserved, at any other point of the motion is the sum of elastic potential energy and kinetic energy:
(2)
where x is the displacement, m the mass, and v the speed.
We want to know the displacement x at which the elastic potential energy is 1/3 of the kinetic energy:
Using (2) we can rewrite this as
And using (1), we find
Substituting into the last equation, we find the value of x:
B)
In this case, the kinetic energy is 1/10 of the total energy:
Since we have
we can write
And so we find: