The force it applies.

Classical Mechanics Level 5

Figure above is an overhead view of a rigid rod that turns about a vertical axle until the identical rubber stoppers A and B are forced against rigid walls at distances $r_{A} = 7$ $cm$ and $r_{B} = 4$ $cm$ from the axle. Initially the stoppers touch the walls without being compressed. Then force $\vec{F}$ of magnitude $220$ $N$ is applied perpendicular to the rod at a distance $R = 5$ $cm$ from the axle. Find the magnitude of the force compressing Stopper A.

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The answer is 119.0.

1 solution

Nathanael Case
Sep 7, 2014

This problem should accept the answer of 118!

Here's the solution:

You have the torque equation:

$FR=f_ar_a+f_br_b$

Let's say the rod moves through an angle $d\theta$ when the stoppers are compressed. Now let's assume the force from the stoppers is proportional to the distance that they are compressed.

That gives us: $kr_ad\theta=f_a$ and $kr_bd\theta=f_b$

But since they are identical, they will have the same constant of proportionality ( $k$ ) so you get the relationship:

$\frac{f_a}{r_a}=\frac{f_b}{r_b}$

Now you have two equations and two unknowns so you can solve for $f_a$ and $f_b$ like any other system of equations.

I won't show the algebra, but you will find that $f_a$ , to the nearest integer, is 118N.

If you round it to the correct number of significant digits, then you get 120N

A side note:

You may have been tempted to write the equation

$f_a=F+f_b$

because the rod is not moving.... But this equation assumes that the axle applies no force on the rod! Which is not true...

Nathanael Case - 6 years, 9 months ago

@Nathanael Case , where were you? I think you have opened brilliant after a long period of time. Please reply. :D

satvik pandey - 6 years, 7 months ago

Yes, I stopped doing physics for a while. Other things in life needed my attention. I am still not doing much physics, but I am at least doing a little bit again.

Nathanael Case - 6 years, 7 months ago

I agree with you. Now they should accept both 118 and 120 N. And even 118 is not exact it is a rounded answer

Rohit Shah - 6 years, 6 months ago

I did the same...

manish bhargao - 6 years, 3 months ago

I totally agree with Natthanael the accepted answer is less correct then the answers I submitted. If we are suppose to round answers then that should be stipulated in the question. I calculated the correct answer and submitted both 118 and then 119 which were both closer to the correct answer then 120. The statement “the answer is an integer is misleading and not true”

Darryl Dennis - 6 years, 3 months ago

In future, if you spot any errors with a problem, you can “report” it by selecting the “dot dot dot” menu in the lower right corner. You will get a more timely response that way.

I have updated this question so that answers from 117-121 are marked correct.

Calvin Lin Staff - 6 years, 3 months ago

The force it applies.

The answer is 119.0.

1 solution

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