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1. At the local playground, a 16 kg child sits on the end of a horizontal teeter-totter, 1.5m from the pivot point. On the other side of the pivot an adult pushes straight down on the teeter-totter with a force of 95 N. In which direction does the teeter-totter rotate if the adult applies the force of a distance (a) 3.0 m, (b) 2.5 m, or (c) 2.0 m from the pivot?
2. A person holds a ladder horizontally at its center. Treating the ladder as a uniform rod of length 3.25 m and a mass 8.40 kg, find the torque the person must exert on the ladder to give it an angular acceleration of 0.322 radians/seconds squared.
3. A school yard teeter-totter with a total length of 5.2 m and a mass of 36 kg is pivoted at its center. A 18 kg child sits on one end of the teeter totter.
(a) Where should a parent push vertically downward with a force of 210 N in order to hold the teeter-totter level?
(b) Where should the parent push with a force of 310 N?
(c) How would your answers to parts (a) and (b) change if the mass of the teeter-totter were doubled? Explain
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Find the maximum rate of change of a function f = 12x 2 + yz2 with respect to distance at point P(-1, 0, 1). Determine the rate of change of f in the x, y, and z directions. What is the rate of change of f in the direction of point Q(1, 1, 1) from P..
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