Hibbeler cap4 solucionario

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4 Solutions 44918

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

•4–1. If A, B, and D are given vectors, prove thedistributive law for the vector cross product, i.e., A : (B + D) = (A : B) + (A : D).

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission inwriting from the publisher.

4–2. Prove the triple A # B : C = A : B # C.

scalar

product

identity

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means,without permission in writing from the publisher.

4–3. Given the three nonzero vectors A, B, and C, show that if A # (B : C) = 0, the three vectors must lie in the same plane.

*4–4. Two men exert forces of F = 80 lb and P = 50 lb on the ropes. Determine the moment of each force about A. Which way will the pole rotate, clockwise or counterclockwise?

P

6 ft

F 45
3 5 4

B

12 ftC A

•4–5. If the man at B exerts a force of P = 30 lb on his rope, determine the magnitude of the force F the man at C must exert to prevent the pole from rotating, i.e., so the resultant moment about A of both forces is zero.

P

6 ft

F 45
3 5 4

B

12 ft

C A

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© 2010 Pearson Education, Inc., Upper Saddle River,NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

4–6. If u = 45°, determine the moment produced by the 4-kN force about point A.

3m A 0.45 m u 4 kN

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Page 194© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

4–7. If the moment produced by the 4-kN force about point A is 10 kN # m clockwise, determine the angle u, where 0°… u … 90°.

3m A 0.45 m u 4 kN

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may be reproduced, in any form or by any means, without permission in writing from the publisher.

*4–8. The handle ofthe hammer is subjected to the force of F = 20 lb. Determine the moment of this force about the point A.

F 30

5 in. 18 in. A B

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© 2010 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected under all copyright laws as they currently exist. No portion of this material may bereproduced, in any form or by any means, without permission in writing from the publisher.

•4–9. In order to pull out the nail at B, the force F exerted on the handle of the hammer must produce a clockwise moment of 500 lb # in. about point A. Determine the required magnitude of force F.

F 30

5 in. 18 in. A B

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