A bicyclist notes that the pedal sprocket has a radius of rp = 9.5 cm while the wheel sprocket has a radius of rw = 4.5 cm. The
1 answer:
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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:
Lower resistivity means higher conductivity: among these materials, the best conductor is silver, therefore it must be the material with lowest resistivity among those. We can also have a look at the value of resistivity of the different materials listed in the problem, to check our answer. The resistivities of the materials are the following:
Wood:
Salt water:
Silver:
Lead:
<span>We see that the material with lowest resistivity among those is silver, therefore the correct answer is silver.</span>
Wood:
Salt water:
Silver:
Lead:
<span>We see that the material with lowest resistivity among those is silver, therefore the correct answer is silver.</span>