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# A box of mass 21 kg sits on an inclined surface with an angle of 10 degrees. What is the component of the weight of the box along the surfac

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A box of mass 21 kg sits on an inclined surface with an angle of 10 degrees. What is the component of the weight of the box along the surface?

physics
Guest May 21, 2015

#5
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Melody, it is the "mg" vector that constitutes the hypotenuse of the right-angled triangle, not the  "mgsinα" line  (I didn't attempt to draw the two magnitudes to scale; I probably should have done!).

To convince yourself that the component along the slope is mgsinα think of the limit when α = 0.  The component along the "slope" must then be zero.

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Alan  May 25, 2015
#1
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21sin10. The force component along the slope is always mg sin theta where theta is the angle of the slope,m is the mass of the object and g is the force of gravity.

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I have dug up this pic

okay - I think I have it

Melody  May 25, 2015
#3
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m = 21 kg

α = 10°

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Alan  May 25, 2015
#4
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Thanks Alan but I am having problems with this :/

I can see that the two angles labelled theta in the first my pic are equal.

and

i can see using the second theta in my pic that

sin(theta)=weight down slope/mg      so

weight down slope = mg*sin(theta)

BUT

If I use the same angle which you have labeled alpha then

sin(alpha)=mg/weight down the slope

weight down the slope = mg/sin(alpha)

Since I can see that these 2 angles are indeed equal I am totally confused by these 2 different outcomes.

What is wrong with my logic :/

Melody  May 25, 2015
#5
+27061
+10

Melody, it is the "mg" vector that constitutes the hypotenuse of the right-angled triangle, not the  "mgsinα" line  (I didn't attempt to draw the two magnitudes to scale; I probably should have done!).

To convince yourself that the component along the slope is mgsinα think of the limit when α = 0.  The component along the "slope" must then be zero.

.

Alan  May 25, 2015
#6
+93691
0

ok that makes sense Alan.   Thanks

So I have to remember that the gravitational force is the hypotenuse!    I shall try

Melody  May 25, 2015