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Unformatted text preview: Chapter 7 Problems 1, 2 , 3 = straightforward, intermediate, challenging Section 7.2 Work Done by a Constant Force 1. A block of mass 2.50 kg is pushed 2.20 m along a frictionless horizontal table by a constant 16.0-N force directed 25.0 below the horizontal. Determine the work done on the block by (a) the applied force, (b) the normal force exerted by the table, and (c) the gravitational force. (d) Determine the total work done on the block. 2. A shopper in a supermarket pushes a cart with a force of 35.0 N directed at an angle of 25.0 downward from the horizontal. Find the work done by the shopper on the cart as he moves down an aisle 50.0 m long. 3. Batman, whose mass is 80.0 kg, is dangling on the free end of a 12.0-m rope, the other end of which is fixed to a tree limb above. He is able to get the rope in motion as only Batman knows how, eventually getting it to swing enough that he can reach a ledge when the rope makes a 60.0 angle with the vertical. How much work was done by the gravitational force on Batman in this maneuver? 4. A raindrop of mass 3.35 10 5 kg falls vertically at constant speed under the influence of gravity and air resistance. Model the drop as a particle. As it falls 100 m, what is the work done on the raindrop (a) by the gravitational force and (b) by air resistance? Section 7.3 The Scalar Product of Two Vectors 5. Vector A has a magnitude of 5.00 units, and B has a magnitude of 9.00 units. The two vectors make an angle of 50.0 with each other. Find AB . 6. For any two vectors A and B , show that AB = A x B x + A y B y + A z B z . ( Suggestion: Write A and B in unit vector form and use Equations 7.4 and 7.5.) Note: In Problems 7 through 10, calculate numerical answers to three significant figures as usual. 7. A force F = 6 i 2 j ( 29 N acts on a particle that undergoes a displacement r = 3 i + j ( 29 m . Find (a) the work done by the force on the particle and (b) the angle between F and r . 8. Find the scalar product of the vectors in Figure P7.8. Figure P7.8 9. Using the definition of the scalar product, find the angles between (a) A = 3 i - 2 j and B = 4 i 4 j ; (b) A = 2 i + 4 j and B = 3 i 4 j + 2 k ; (c) A = i - 2 j + 2 k and B = 3 j + 4 k ....
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