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lecture 20 - Lecture 20 Statics 1 The conditions for...

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1 Lecture 20 Statics
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2 The conditions for equilibrium are 0 0 = = τ F To have static equilibrium p = 0 and L = 0 too.
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3 Center of gravity If g is the same for all points within a body, then r cm = r cg . An object that is 30 km tall will have a 1% variation in g over its length.
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4 Consider a beam on a support that is beneath the beam’s center of gravity. The FBD for the beam: F sb F eb Apply N2L 0 eb sb = - = F F F y y x
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5 What about the torque? 0 2 2 eb sb = - = F L F L τ If the axis is chosen at the point of contact between the beam and support, the lever arm is zero for both forces, and the net torque is zero. This condition will be met for any other axis as well. Choose the axis at the left end of the beam: This implies that F sb = F eb , the same as N2L.
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6 What if the support is moved a distance x to the left? x The FBD for the beam: F sb F eb Apply N2L 0 eb sb = - = F F F y y x
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7 What about the torque? 0 eb - = xF τ Chose the axis at the support: And the beam is not in equilibrium.
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