M1 question... Watch

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Magician
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#1
Report Thread starter 14 years ago
#1
Hey, here is the question:-

A body of mass 2kg is held in limiting equilibrium on a rough horizontal plane inclined at 20 deg. to the horizontal by a force Y (at an angle 45deg. to the horizontal). Coefficient of friction = 0.2. Model as particle and find Y when particle is on the point of slipping down the plane.

Here's what I have done:-

Resolving perpendicular to the plane:-

R - 2gcos 20 - Y sin 65 = 0
R = 2gcos 20 + Y sin 65

Parallel to plane : -

F + Ycos65 - 2gsin 20 = 0
F = 2gsin20 - Y cos 65

Since in lim. equi. F = mu.R

2gsin20 - Y cos 65 = 0.4gcos20 + 0.2Y sin 65
-0.603879819 Y = -3.019999736
Y = 5.00097.....N

but the answer given is 3.67N
Aitch
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#2
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#2
(Original post by Mathemagician)
Hey, here is the question:-

A body of mass 2kg is held in limiting equilibrium on a rough horizontal plane inclined at 20 deg. to the horizontal by a force Y (at an angle 45deg. to the horizontal). Coefficient of friction = 0.2. Model as particle and find Y when particle is on the point of slipping down the plane.

Here's what I have done:-

Resolving perpendicular to the plane:-

R - 2gcos 20 - Y sin 65 = 0
R = 2gcos 20 + Y sin 65

Parallel to plane : -

F + Ycos65 - 2gsin 20 = 0
F = 2gsin20 - Y cos 65

Since in lim. equi. F = mu.R

2gsin20 - Y cos 65 = 0.4gcos20 + 0.2Y sin 65
-0.603879819 Y = -3.019999736
Y = 5.00097.....N

but the answer given is 3.67N

Isn't the other angle 25?

Check it - my sketch may be wrong - I'm not sure I have the angles right on the sketch myself.

Aitch
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Christophicus
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#3
Report 14 years ago
#3
Resolve perpendicular to plane
R - 2gcos20 + Ysin 25 = 0
R = 2gcos20 - Ysin 25

Resolve parallel to plane
F + Ycos 20 - 2gsin20 = 0
F = 2gsin20 - Ycos25

mu = 0.2

F = mu(R) in limiting equilibrium.
F = 0.2R

2gsin20 - Ycos25 = 0.2(2gcos20 - Ysin25)
2gsin20 - Ycos25 = 0.4gcos20 - 0.2sin25Y
2gsin20 - 0.4gcos20 = -0.2sin25Y + cos25Y
3.01999736 = 0.821784134Y
Y = 3.67N
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Magician
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#4
Report Thread starter 14 years ago
#4
(Original post by Aitch)
Isn't the other angle 25?

Check it - my sketch may be wrong - I'm not sure I have the angles right on the sketch myself.

Aitch
why is it 25?
Christophicus
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#5
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#5
(Original post by Mathemagician)
why is it 25?
see my solution.
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Christophicus
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#6
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#6
The angle is 45 degrees from the horizontal, so the angle the force Y makes with the plane is 45 - 20 = 25 degrees.
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