Problems07 - Chapter 7 Problems 1 2 3 = straightforward...

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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  A∙B . 6. For any two vectors  A  and  B , show that  A∙B  =  A x B x  +  A y B y   A z B z . ( Suggestion:  Write  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 ˆ  – 2 ˆ  ( 29 N  acts on a  particle that undergoes a displacement     r = 3 ˆ  + ˆ  ( 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.
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Figure P7.8 9. Using the definition of the scalar product,  find the angles between (a)     A = 3 ˆ  - 2 ˆ   and     B = 4 ˆ  – 4 ˆ  ; (b)     A = – 2 ˆ  + 4 ˆ   and     B = 3 ˆ  – 4 ˆ  + 2 ˆ  ; (c)     A = ˆ  - 2 ˆ  + 2 ˆ    and     B = 3 ˆ  + 4 ˆ  .
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