Why does light change its velocity (or slows down) when it encounters a glass lens?
1 answer:
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A) The change in internal chemical energy is
B) The time needed is 1 minute
Explanation:
First of all, we start by calculating the power output of you and the bike, given by:
where
F = 80 N is the force that must be applied in order to overcome friction and travel at constant speed
v = 8.0 m/s is the velocity
Substituting,
The energy output is related to the power by the equation
where:
P = 640 W is the power output
E is the energy output
is the time elapsed
Solving for E,
Since the body is 10% efficient at converting chemical energy into mechanical work (which is the output energy), this means that the change in internal chemical energy is given by
B)
From the previous part, we found that in a time of
t = 30 min
the amount of internal chemical energy converted is
Here we want to find the time t' needed to convert an amount of chemical energy of
So we can setup the following proportion:
And solving for t',
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Answer:
a) 8.83*10⁵ m/s b) 2.80*10⁶ m/s
Explanation:
a) Assuming no other forces acting on the proton, the acceleration on it is produced by the electric field.
By definition, the force due to the electric field is as follows:
F = q*E = e*E (1)
where e is the elementary charge, the charge carried by only one proton, and is e = 1.6*10⁻¹⁹ C.
According to Newton's 2nd law, this force is at the same time, the product of the mass of the proton, times the acceleration a:
F = mp*a (2)
From (1) and(2), being left sides equal, right sides must be equal too:
Solving for a:
⇒ a = 1.3*10¹³ m/s²
As we have the value of a (which is constant due to the field is uniform), the displacement x, and we know that the initial velocity is 0, in order to get the value of the speed, we can use the following kinematic equation:
Replacing by v₀ = 0, a= 1.3*10¹³ m/s² and x = 0.03 m, we can find vf as follows:
⇒ vf = 8.83*10⁵ m/s
b) We can just repeat the equation from above, replacing x=0.03 m by x=0.3 m, as follows:
⇒ vf = 2.80*10⁶ m/s