Exercise 2.36 Two sticks and a wall

Two sticks are connected, with hinges, to each other and to a wall. The bottom stick is horizontal and has length LL, and the sticks make an angle of θ\theta with each other, as shown in Figure above. If both sticks have the same mass per unit length, ρ\rho, find the horizontal and vertical components of the force that the wall exerts on the top hinge.

Also show that the magnitude goes to infinity for both θ\theta00 and θ\thetaπ2\frac{\pi}{2}

Note by Beakal Tiliksew
5 years, 4 months ago

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In the above figure, I have marked all the forces that are present in the system. Let the masses of the two rods be m1\displaystyle m_1 and m2\displaystyle m_2.

Thus,
m1=ρLsecθm_1 = \rho L\sec\theta m2=ρLm_2 = \rho L

Considering the torque about the point A,
h1(Ltanθ)=(m1+m2)gL2h_1(L\tan\theta) = (m_1+m_2)g\frac{L}{2}

h1(Ltanθ)=ρL(1+secθ)gL2h_1(L\tan\theta) = \rho L (1+\sec\theta)g\frac{L}{2}

h1=ρ1+secθtanθgL2\boxed{h_1 = \rho\frac{1+\sec\theta}{\tan\theta}\frac{gL}{2}}

Ill do the vertical force later..Ill post it as a comment

Anish Puthuraya - 5 years, 4 months ago

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Nice explanation

Mardokay Mosazghi - 5 years, 4 months ago

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Why are there no forces at the hinge joining the 2 sticks ??

CH Nikhil - 4 years, 2 months ago

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There are forces at the hinge joining the sticks, but they are internal forces. So, they cancel each other off..

Anish Puthuraya - 4 years, 2 months ago

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@Anish Puthuraya Got it ! Thanks a lot !!

CH Nikhil - 4 years, 2 months ago

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do you know any good book with exersises in rotational dynamics ;

aris nikolaidis - 4 years, 9 months ago

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Try IE Irodov or Krotov

Pranjal Jain - 4 years, 9 months ago

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The vertical force can be found using the pivot point B. It is -(rholg/2)(1+2sec(theta)).

Harsh Bhardwaj - 1 year, 3 months ago

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