How do I prove that a = v * dv/dx?

1 answer:

6 0

Your book has applied the chain rule to produce:
dv/dt = dv/dx * dx/dt
Now, we can get dv/dx by:
1) Differentiate
x = vt, with respect to v.
dx/dv = t
Now, if we take the inverse of this, we can obtain dv/dx
dv/dx = 1/t
This is also proven by the fact that dv/dx is the change in velocity and if you multiply it by dv/dx, which is equivalent to dividing by the change in time, as we just proved, then you obtain acceleration.

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Need help solving this question.

MatroZZZ [7]

Answer:

See the answers below.

Explanation:

to solve this problem we must make a free body diagram, with the forces acting on the metal rod.

The center of gravity of the rod is concentrated in half the distance, that is, from the end of the bar to the center there is 40 [cm]. This can be seen in the attached free body diagram.

We have only two equilibrium equations, a summation of forces on the Y-axis equal to zero, and a summation of moments on any point equal to zero.

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Now we perform a sum of moments equal to zero around the point of attachment of the string with the metal bar. Let's take as a positive the moment of the force that rotates the metal bar counterclockwise.

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