F-sol - Chapter F Problems Blinn College Physics 2425 Terry...

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Unformatted text preview: Chapter F - Problems Blinn College - Physics 2425 - Terry Honan Problem F.1 A 600 N force pushes a refrigerator 8 m along a floor. What is the work done by the force? Solution to F.1 For a constant force in one dimension: W = F D x = 600 μ 8 = 4800 J Problem F.2 Junior lifts a 20 N weight slowly (assume zero acceleration at all times) a distace of 1.5 m. What is the work done by Junior and what is the work done by gravity? Solution to F.2 The lifting force is the same as the weight in magnitude. W = F D x is the work done by a constant force in one dimension. F and D x should be viewed as one dimensional vectors; the direction of a one dimensional vector is its sign. W Junior = F D x = 20 μ 1.5 = 30 J and W grav = F D x = H- 20 L μ 1.5 = - 30 J Problem F.3 Consider the vectors A = X- 2, 5,- 3 \ and B = X- 1, 0, 2 \ . (a) What is the angle between the two vectors? (b) What is the angle between A and the positive z axis? Solution to F.3 The dot product has A × B = A B cos q and A × B = A x B x + A y B y + A z B z as alternative definitions. (a) To find the angle between two vectors we equate the two definitons. To evaluate this dot product,. since we are given the compo- nents of the two vectors, the second is the definition we need A × B = A x B x + A y B y + A z B z = H- 2 L H- 1 L + 5 ÿ + H- 3 L ÿ 2 = - 4 The the magnitudes of the two vectors are A = 2 2 + 5 2 + 3 2 = 38 and B = 1 + + 2 2 = 5 . Now we can find the angle. A × B = A B cos q ï q = cos- 1 A × B A B = cos- 1- 4 38 5 = 106.9 ° (b) The angle between a vector and the z axis can be by repeating the above procedure replacing B with e ` z . Generally, the dot product of any vector and a unit vector gives the component of the vector in the direction of the unit vector. A × e ` z = A x + A y + A z 1 = A z = - 3 q = cos- 1 A × e ` z A 1 = cos- 1- 3 38 1 = 119.1 ° Problem F.4 A 20 N block, initially at rest, is dragged 5 m along a horizontal floor by a rope. The rope has a tension of 12 N and makes an angle of 25 ° above horizontal. A friction force of 9 N acts backward. (a) There are four forces acting: the tension, friction, the normal force and gravity. What is the work done by each force? (b) What is the final speed of the block? Solution to F.4 (a) There are three forces acting on the block: the tension, the normal force and gravity. The work done by a constant force is: W = F × D r ” = F D r cos q . Gravity and the normal force are perpendicular to the direction of motion (horizontal) and thus do zero work. W N = = W grav The tension force does positive work: W T = T D r cos q = 12 μ 5 cos 25 ° = 54.379 = 54.4 J. The friction force f k opposes the direction of motion and does negative work: W f = f k D r cos 180 ° = - f k D r = - 9 μ 5 = - 45 J....
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F-sol - Chapter F Problems Blinn College Physics 2425 Terry...

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