Density through Stress-distance graph!

Classical Mechanics Level 5

Rod of constant cross-section moves towards right with constant acceleration. Graph of stress and distance from left end is given as in figure. If density of material of rod at cross section $1$ is $9 \frac{g}{cm^3}$ . Find density at cross section $2$ in $\frac{g}{cm^3}$ .

The answer is 16.

1 solution

Nishant Rai
May 28, 2015

There is a typo in the question it should be 9 g/cm^3

Kyle Finch - 6 years ago

i made a mistake while writing $\rho_1$ . Now i have edited the problem. $\rho_1 = 9 \dfrac{g}{cm^3}$

Kyle Finch

Nishant Rai - 6 years ago

I came to the same solution (except there is a typo as Kyle said) but what I don't understand is why would the density increase with x? My intuition tells me the density should decrease with x, and the slope should be decreasing with x.

Can you please explain why the density increases with +x instead of decreases?

Nathanael Case - 6 years ago

Yes it is more intuitive to imagine mass accumulating to resist motion and hence more mass concentrated at the tip (x=0). This would mean higher density near x=0. But this is a rigid body and cannot deform and application of Newton's laws gives higher density at x=L.

Shubham Maurya - 5 years, 6 months ago

I agree with you , I think density should be max at x = 0.

Ankit Kumar Jain - 3 years, 2 months ago

Density through Stress-distance graph!

The answer is 16.

1 solution

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