10-kg box is sliding across an ice rink at 10 m/s . A skater exerts a constant force of 10 N against it. How long will it take f
1 answer:
You might be interested in
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: