B 2R
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A uniform rod AB of length 2R rests inside a hemispherical bowl of radius R as shown. Neglecting friction, determine the angle θ corresponding to equilibrium.
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- A force, T, is exerted on a horizontal beam at point B at an angle 8 with respect to the horizontal as shown. The magnitude of the torque created by force T about point C, is given by E A AT B W₁ O W₁yo-yo with an inner cylinder of r = 3.5 cm and outer radius of R = 6.50cm is at rest on a theta = 30 degree incline. Itis held in place by friction and the tension in the string that is wrapped around its inner cylinder, as shown in the figure. Assume that the positive x-direction points down the incline. Determine the friction force if the mass of the yo-yo is 420g.Don't provide handwritten solution.
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- 2. Consider the curve ø(t) = (t² – 4t + 2, cos(t²), ' sin(t²)) for t E (0, 1). (a) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M 2. (b) Find the work required to bend a straight rod into ø, assuming a stiff- ness of M(x, y, z) = /1+ x² + y² + 2².Two uniform planks, each of mass m = 7.45 kg and length L = 2.51 m, are connected by a hinge at the top and by a chain of negligible mass attached at their centers, as shown in the figure. The assembly will stand upright, in the shape of an A, on a frictionless surface without collapsing. If the chain has the length 0.81 m, find each of the following: a) the absolute value of the tension in the chain, b) the absolute magnitude of the force on the hinge of each p lank