6 - Circular Motion and Other Applications of Newton's Laws

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Unformatted text preview: If a 45.0-kg child sits on the horizontal ﬂoor of the merry-go-round 3.00 m from the center, ﬁnd (a) the child’s acceleration and (b) the horizontal force of friction that acts on the child. (c) What minimum coefﬁcient of static friction is necessary to keep the child from slipping? 25. A 0.500-kg object is suspended from the ceiling of an accelerating boxcar as was seen in Figure 6.13. If a 3.00 m/s2, ﬁnd (a) the angle that the string makes with the vertical and (b) the tension in the string. 26. The Earth rotates about its axis with a period of 24.0 h. Imagine that the rotational speed can be increased. If an object at the equator is to have zero apparent weight, (a) what must the new period be? (b) By what factor would the speed of the object be increased when the planet is rotating at the higher speed? (Hint: See Problem 53 and note that the apparent weight of the object becomes zero when the normal force exerted on it is zero. Also, the distance traveled during one period is 2 R, where R is the Earth’s radius.) 27. A person stands on a scale in an elevator. As the elevator starts, the scale has a constant reading of 591 N. As the elevator later stops, the scale reading is 391 N. Assume the magnitude of the acceleration is the same during starting and stopping, and determine (a) the weight of the person, (b) the person’s mass, and (c) the acceleration of the elevator. 28. A child on vacation wakes up. She is lying on her back. The tension in the muscles on both sides of her neck is 55.0 N as she raises her head to look past her toes and out the motel window. Finally, it is not raining! Ten minutes later she is screaming and sliding feet ﬁrst down a water slide at a constant speed of 5.70 m/s, riding high on the outside wall of a horizontal curve of radius 2.40 m (Fig. P6.28). She raises her head to look forward past her toes; ﬁnd the tension in the muscles on both sides of her neck. 176 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws 40.0 m/s 20.0 m 40.0° 620 kg Figure P6.34 Figure P6.28 35. 29. A plumb bob does not hang exactly along a line directed to the center of the Earth, because of the Earth’s rotation. How much does the plumb bob deviate from a radial line at 35.0° north latitude? Assume that the Earth is spherical. 36. (Optional) Section 6.4 Motion in the Presence of Resistive Forces 30. A sky diver of mass 80.0 kg jumps from a slow-moving aircraft and reaches a terminal speed of 50.0 m/s. (a) What is the acceleration of the sky diver when her speed is 30.0 m/s? What is the drag force exerted on the diver when her speed is (b) 50.0 m/s? (c) 30.0 m/s? 31. A small piece of Styrofoam packing material is dropped from a height of 2.00 m above the ground. Until it reaches terminal speed, the magnitude of its acceleration is given by a g bv. After falling 0.500 m, the Styrofoam effectively reaches its terminal speed, and then takes 5.00 s more to reach the ground. (a) What is the value of the consta...
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## This document was uploaded on 09/19/2013.

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