Mathematical Methods in the Physical Sciences

3rd Edition

ISBN: 9780471198260

Author: Mary L. Boas

Publisher: Wiley, John & Sons, Incorporated

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Textbook Question

Chapter 6.3, Problem 4P

For Problems 2 to 6, given A = i + j − 2 k , B = 2 i − j + 3 k , C = j − 5 k :

Let O be the tail of B and let A be a force acting at the head of B .

Find the torque of A about O ; about a line through O perpendicular to the plane of A and B ; about a line through O parallel to C .

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Chapter 6.3, Problem 3P

Chapter 6.3, Problem 5P

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3. Find the magnitude and direction of the resultant of a 10 N force that acts an angle 40° clockwise from the +x-axis, a 7 N force that acts at an angle of 180° clockwise from the +y-axis, and 5 N force that acts at an angle of 90° clockwise from the +y-axis.

On the graph to the right, draw a coordinate axis. Draw in the two force vectors. Show by adding the vectors graphically that the net force on the central ring is zero. Verify this algebraically by showing that the sum of the. components is also zero. L +) = N the position. Now, notice that you can slide the ring back and forth along the r axis, placing it at any distance, and the ring will stay in place. This means that every point along the r axis is an equilibrium point. Explain why this is the case. The forces Cancel it does not matter FYEN Now we're going to change the axes. Remove the two pulleys, and place them at angles of 90° and 270°, respectively. Keeping the z axis along = 0, we've now placed the forces along the y axis. Repeat the earlier analysis with the new forces. 1D Trial 2 Results Force Magnitude (N) Direction (6) 0297 F₁ F₂ 0.48A/ 1 80 13 JEN Vector 0.294160 GrMB.NK 1800 F 11800

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Chapter 6 Solutions

Mathematical Methods in the Physical Sciences

Ch. 6.3 - If A=2ijk,B=2i3j+k,C=j+k, find (AB)C,A(BC),(AB)C,...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - For Problems 2 to 6, given A=i+j2k,B=2ij+3k,C=j5k:...Ch. 6.3 - A force F=2i3j+k acts at the point (1,5,2). Find...Ch. 6.3 - Prob. 8P Ch. 6.3 - Prob. 9P Ch. 6.3 - In Figure 3.5, let r be another vector from O to...

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