A government agency estimated that air bags have saved over 14,000 lives as of April 2004 in the United States. (They also state
1 answer:
To solve this problem it is necessary to apply the concepts related to momentum, momentum and Force. Mathematically the Impulse can be described as
Where,
F= Force
t= time
At the same time the moment can be described as a function of mass and velocity, that is
Where,
m = mass
v = Velocity
From equilibrium the impulse is equal to the momentum, therefore
PART A) Since the body ends at rest, we have the final speed is zero, so the momentum would be
Therefore the magnitude of the person's impulse is 1125Kg.m/s
PART B) From the equation obtained previously we have that the Force would be:
Therefore the magnitude of the average force the airbag exerts on the person is 45000N
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Answer:
1.
2.
3.The results from part 1 and 2 agree when r = R.
Explanation:
The volume charge density is given as
We will investigate this question in two parts. First r < R, then r > R. We will show that at r = R, the solutions to both parts are equal to each other.
1. Since the cylinder is very long, Gauss’ Law can be applied.
The enclosed charge can be found by integrating the volume charge density over the inner cylinder enclosed by the imaginary Gaussian surface with radius ‘r’. The integration of E-field in the left-hand side of the Gauss’ Law is not needed, since E is constant at the chosen imaginary Gaussian surface, and the area integral is
where ‘h’ is the length of the imaginary Gaussian surface.
2. For r> R, the total charge of the enclosed cylinder is equal to the total charge of the cylinder. So,
3. At the boundary where r = R:
As can be seen from above, two E-field values are equal as predicted.