Question about torque in TBR

[Novis619]

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Here is the question:

The answer is B. Lmgcos(theta). Can someone please explain why? Thanks.

 

[jetsfan1234]

Complete the right triangle by drawing a line straight down from the ball. this represents the weight vector = mg.

Now draw another line, through the ball, PERPENDICULAR to the incline. this represents the y axis. Let the incline itself represent the x axis.

At any point in time, the Y component of mg is the force that is perpendicular to the lever arm. This is the force that produces the torque. The moment arm is equal to L.

Using trigonometry you can show that the Y component of the weight force = mgcos(theta). Its a lot similar to inclined plane geometry.

Now put everything together. Torque = R x F = L x mgcostheta

 

[frochocinco]

the easiest way to remember this is, like jetsfan1234 just said, think of this as an inclined plane problem and remember that your mg vector is ALWAYS the hypotenuse. Then, the rest should be pretty straightforward

and btw, i hate the Jets and I'm agreeing with this guy, so we must be on to something!

 

[sazerac]

MCAT method:

Torque is force x distance from axis. Answers C and D don't take distance into account, so eliminate them.

Is it sin or cos theta? Assume theta is almost 0. The rod will be superfluous then. Thus are going to want a result that is basically mg when theta is near 0. Thus it must be cos theta.

Total problem solving time: 6 seconds.

 

[stevvo111]

MCAT method:

Torque is force x distance from axis. Answers C and D don't take distance into account, so eliminate them.

Is it sin or cos theta? Assume theta is almost 0. The rod will be superfluous then. Thus are going to want a result that is basically mg when theta is near 0. Thus it must be cos theta.

Total problem solving time: 6 seconds.

Smart stuff, it's important to learn like, but unfortunately most students (including myself at times) trust getting the answer through more laborious methods as opposed to the quicker more efficient way (which we have been taught over the years to almost always lead to the wrong answer).

I wish a response like this was given for all of the answers in all of the books and practice tests. It really shows how we need to be logical above all to solve any question.