12.Two masses are arranged as shown on a ramp that makes an angle of 36° with the horizontal. Mass m1 is twice mass m2
. What is the minimum coefficient of static friction required between mass m1 and the ramp to ensure equilibrium?
Answers
Force M2 exerts on tension T
T = M2 g
T = M1 g sin theta - M1 g u cos theta
Note that M1 g is exerted down the plane while the frictional force opposes this motion and will be directed in the opposite direction of M1 g
M2 g = M1 g sin theta - u M1 g cos theta
1 = 2 sin 36 - u 2 cos 36
.5 = sin 36 - u cos 36
u = (sin 36 - .5) / cos 36 = .108
Any friction less that this will result in sliding
"1.7456" would be the minimum coefficient of static friction required.
Given:
Angle,
[tex]\Theta = 30^{\circ}[/tex]Mass,
[tex]m_2 =2 m_1[/tex]To keep the system in equilibrium forces acting on mass "[tex]m_1[/tex]" must balance forces acting on "[tex]m_2[/tex]".
That's,
→ [tex]Forces \ on \ m_1 \ downward \ along \ ramp = Forces \ on \ m_2 \ downwards[/tex]
or,
→ [tex]m_1 g Sin \Theta + \mu_s m_1 g Cos \Theta =m_2 g[/tex]
Thus,
→ [tex]\mu_s = \frac{m_2 g - m_1 g Sin \Theta}{m_1 g Cos \Theta}[/tex]
[tex]= \frac{m_2-m_1 Sin \ 36^{\circ}}{m_1 Cos \Theta}[/tex]
hence,
→ [tex]\mu_s = \frac{2 m_1 - m_1 Sin \ 36^{\circ}}{m_1 Cos \ 36^{\circ}}[/tex]
[tex]= 1.7456[/tex]
Thus the above answer is right.
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What is speed ?"Speed is the distance traveled per unit of time. It is how fast an object is moving. Speed is the scalar quantity that is the magnitude of the velocity vector. It doesn't have a direction."
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Answer:
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Answer:
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Explanation:
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Answer:
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