TBR online Mechanics : Ramp question

[hmania]

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I could only fit so much on the screen, but other relevant details are: mass of boat 5000kg, the coefficient of static friction 0.4.

I was thinking to use F= (coef. of static friction)mgsin. I thought since this force of friction counters that of tension of the F2. I am confused to why the explanation uses Cosine which corresponds to the normal force.


Help!🙁

 

[indianjatt]

First you have to determine whether or not you have surpassed the maximum static friction (whether you have applied enough force in order to get the boat moving).

The maximum force of static friction = Normal force * meu(s)

In this case the normal force = mg cos theta.

So the maximum force of static friction = 5000 kg * 10 m/s^2 * 0.866 * .4 = > 10kN.

So because you have not applied a force greater than the maximum force of static friction, the frictional force will simply equal the applied force.