A child is swinging back and forth on a tire swing that is attached to a tree br

Question

A child is swinging back and forth on a tire swing that is attached to a tree branch by a single rope. The child swings from right to left and has a speed of 2 m/s at a position just to the right of the lowest position, and the same speed of 2 m/s at a position just to the right of the lowest position. Three students are discussing the tension in the rope at the bottom of the swing (the lowest position). Ayliah: At the bottom of the swing, the child will be moving exactly horizontally. Since she is not moving vertically at that instant, the vertical forces cancel. The tension in the rope at that instead equals the weight. Blaise: Just looking at the velocity vectors, the change in velocity points upward between A and B. So that is the direction of the acceleration, and also of the net force. To get a net force pointing upward, the tension would have to be a greater than the weight. Conrad: But there aren't just two forces acting on her at the bottom of the swing. Since she's moving in a circle, there's also the centripetal force, which acts toward the center of the circle. Since both the tension and the centripetal force point upward, and the weight points downward, to get zero net force the tension actually has to be less than the weight. The tension plus the centripetal force equals the weight. Which, if any, of these students do you agree with? Ayliah: _____ Blaise: _____ Conrad: _____ None of them: _____ Explain your reasoning

Explanation / Answer

ayliah = wrong

blaise = correct

T = m*v*v/r + mg

cpnrad = correct

A particle may have orbital angular momentum (like an electron orbiting around the nucleus in an atom or like the earth orbiting the sun) or it may have intrinsic angular momentum (like the earth spinning on its own axis or like the spin angular momentum of the elementary particle). When one goes to the microscopic level of elementary particles, angular momentum is quantized, that is only discrete amounts of angular momentum are allowed; for example, if the angular momentum quantum number of a particle is L, its angular momentum is [h/(2?)]?{L(L+1)} where h is Planck's constant. For a spin

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