# PS6 - Physics 16 Problem Set 6 Solutions Y&F Problems 1.55...

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Physics 16 Problem Set 6 Solutions Y&F Problems 1.55. I DENTIFY : For all of these pairs of vectors, the angle is found from combining Equations (1.18) and (1.21), to give the angle as . S ET U P : Eq.(1.14) shows how to obtain the components for a vector written in terms of unit vectors. E XECUTE : (a) and so . (b) . (c) and . E VALUATE : If , . If , . If , and the two vectors are perpendicular. 1.93. I DENTIFY : Find the angle between specified pairs of vectors. S ET U P : Use E XECUTE : (a) (along line ab ) (along line ad ) So (b) (along line ad ) (along line ac ) So E VALUATE : Each angle is computed to be less than in agreement with what is deduced from Fig. 1.43 in the textbook. 6.3. I DENTIFY : Each force can be used in the relation for parts (b) through (d). For part (e), apply the net work relation as S ET U P : In order to move the crate at constant velocity, the worker must apply a force that equals the force of friction, E XECUTE : (a) The magnitude of the force the worker must apply is: (b) Since the force applied by the worker is horizontal and in the direction of the displacement, and the work is:

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(c) Friction acts in the direction opposite of motion, thus and the work of friction is: (d) Both gravity and the normal force act perpendicular to the direction of displacement. Thus, neither force does any work on the crate and (e) Substituting into the net work relation, the net work done on the crate is: E VALUATE : The net work done on the crate is zero because the two contributing forces, are equal in magnitude and opposite in direction.
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