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Chapter 11 Problems University of Colorado Coorado Springs11章的问题科罗拉多大学科罗拉多斯普林斯
Chapter 11 Problems 1, 2, 3 = straightforward, intermediate, challenging Section 11.1 The Vector Product and Torque Given and , calculate the vector product M ( N. 2. The vectors 42.0 cm at 15.0( and 23.0 cm at 65.0( both start from the origin. Both angles are measured counterclockwise from the x axis. The vectors form two sides of a parallelogram. (a) Find the area of the parallelogram. (b) Find the length of its longer diagonal. 3. Two vectors are given by and . Find (a) A ( B and (b) the angle between A and B. 4. Two vectors are given by and , evaluate the quantities (a) cos–1[A · B/AB] and (b) sin–1[|A ( B|/AB]. (c) Which give(s) the angle between the vectors? 5. The wind exerts on a flower the force 0.785 N horizontally to the east. The stem of the flower is 0.450 m long and tilts toward the east, making an angle of 14.0° with the vertical. Find the vector torque of the wind force about the base of the stem. 6. A student claims that she has found a vector A such that . Do you believe this claim? Explain. 7. If |A ( B| = A · B , what is the angle between A and B? 8. A particle is located at the vector position N, and the force acting on it is . What is the torque about (a) the origin and (b) the point having coordinates (0, 6) m? 9. Two forces F1 and F2 act along the two sides of an equilateral triangle as shown in Figure P11.9. Point O is the intersection of the altitudes of the triangle. Find a third force F3 to be applied at B and along BC that will make the total torque zero about the point O. What If? Will the total torque change if F3 is applied not at B but at any other point along BC? Figure P11.9 10. Use the definition of the vector product and the definitions of the unit vectors , , and to prove Equations 11.7. You may assume that the x axis points to the right, the y axis up, and the z axis toward you (not away from you). This choice is said to make the coordinate system right-handed. Section 11.2 Angular Momentum 11. A light rigi
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