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Mathematics 21 Online
OpenStudy (anonymous):

How much force is required to drag a 90 lb. box up this "frictionless" inclined plane? 109 lb. 10 lb. 81 lb. 9 lb.

OpenStudy (anonymous):

OpenStudy (anonymous):

i would have to say a

OpenStudy (anonymous):

hmmmmmm can you explain how can i find this answer?

OpenStudy (mathmale):

Hi, Manny! Only three forces are important here: 1) the weight of the box; 2) the pull of gravity in the direction downward and parallel to the sloping surface, and the unknown force. We aren't given the angle of this ramp; but are given the lengths of the sides of the triangle. Could you figure out the angle from the side lengths and one of the inverse trig functions?

OpenStudy (anonymous):

i don't understand tbh.. i need to figure out how much force will it take to drag a 90lbs box up the incline plan... I'm taking a physical science test

OpenStudy (mathmale):

Have you drawn a free body diagram before?

OpenStudy (anonymous):

no

OpenStudy (mathmale):

Have you seen any sample problems where you have to split a single force into two component forces?

OpenStudy (mathmale):

I'm trying to figure out where you're coming from in terms of understanding the mechanics of this problem, so that I can build upon what you already know.

OpenStudy (anonymous):

idk anything i just want to finish this test that way i can take my sorry retricehome and drink my sorrows away

OpenStudy (anonymous):

sorry a s s * home

OpenStudy (mathmale):

I'll briefly outline the procedure: 1) find the measure of the smallest angle of this triangle; 2) the straight downward force on the box is 90 lb. Box can't fall straight down becasue it's on a ramp. The downward force can be split into two perpendicular forces, one of which is not straight down, but rather downward and parallel to the ramp. Does this ring a bell at all?

OpenStudy (mathmale):

this is an interesting topic, but if you're taking a test right now and if you haven't worked with free body diagrams and component vectors, it'd take some time to explain the problem fully.

OpenStudy (anonymous):

todays my brothers birthday. he just turned 19, he passed away.... all day my minds been dwelling off topic...

OpenStudy (mathmale):

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OpenStudy (mathmale):

My deepest sympathy. Don't see how you could manage to concentrate on math/physics at all on a day like this. So sorry!! What do you want to do? Continue or come back here later, when you're feeling a bit better?

OpenStudy (mathmale):

We can determine the angle that the slope makes with the horizontal using the inverse sine function. That angle would be \[\sin ^{-1}\frac{ H }{ 9H }=\sin ^{-1}\frac{ 1 }{ 9 }\]

OpenStudy (mathmale):

This comes out to about 6 degrees.

OpenStudy (anonymous):

there's always a reason to get back on your feet.. thank you lets continue. hmmmm

OpenStudy (anonymous):

is it 10?

OpenStudy (mathmale):

All right. Sorry again. Does my use of the inverse sine function ring a bell with you? In the triangle given, the side opposite the angle 6 degrees is marked H, and the hypotenuse (length of the ramp) is marked 9H.

OpenStudy (mathmale):

As a matter of fact, the component of that 90 lb in the direction opposite to the pull of the rope is 10 lb, and that asnwers this question. A 10-lb force will pull the box up this ramp if there's no friction.

OpenStudy (mathmale):

So it wasn't even necessary to find the angle in degrees. What you did has worked.

OpenStudy (anonymous):

thanks you you helped me!.

OpenStudy (mathmale):

If I had to write out the answer formally, this is what I'd write:\[F _{e}=(90 lb)\sin \sin ^{-1}\frac{ 1 }{ 9 }=(90 lb) (\frac{ 1 }{ 9 }) = 10 lb\]

OpenStudy (mathmale):

My sympathy, JMC. Hope you can remember the good times you enjoyed with your brother and cherish what you learned from him. Best to you. Over and out.

OpenStudy (mathmale):

Bye, JMC.

OpenStudy (anonymous):

thank you so much my brother Raymond was a MARSOC warrior for the USMC. Soon I'll avenge his death..... and pay a tribute for fallen heaven hound.. Rahhh! thank you mathmale

OpenStudy (mathmale):

What an honor for Raymond to be in the USMC, and for you that he was your bro. Going into the USMC yourself?

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