Homework Assignments for Physics 104

Assignment 1. Due Thursday, February 4, 1999
 

  1.  Join the HyperNews group (link available from our web page).
  2. Post a message under First Homework Assignment. This message should be titled with your name and should include where you are from, what your major is and anything else you wish to share with the class
  3. Come to Professor's Goodman's office (room 4324) and check your name off the list.
Do the following exercises from the book on page 20:

5, 11, 16, 22

Do the following problems from the book on page 21:

1, 3, 10, 11, 12

Solutions to assignment 1
5.  Because the mass of the anvil is larger, the anvil resists
acceleration more than the steel plate, and will not move as much when the
blacksmith strikes a piece of hot metal against it.  The hot metal
consequently gets squeezed between the moving hammer and the stationary
anvil.

11. South.  Stopping (slowing down) requires an acceleration in the
direction opposite to the direction of motion.

16.  The acorn's velocity is not constant; it takes time for it to
accelerate from 0 to -9.8 m/s.  The acorn would only reach the ground in 1
second if it were falling at a constant velocity of 9.8 m/s.  Since it
takes time to speed up to 9.8 m/s, it must take longer than 1 second to
reach the ground.

22. The person must jump up, because gravity will accelerate him
downwards while he is jumping between buildings.

1. F = ma  = 800kg*4m/ss = 3200N

3. v = v_0 + a t = 0 m/s + 3.71 m / s^2 * 3 s = 11.13 m/s

10.   Weight is a force, so
         w = f = ma
         On Earth, a = g = 9.8 m/(s^2)
         w = 60kg*9.8m/ss=588N

11.  When the person stops rising (at the top of the jump) his velocity
is zero.

       v=v_o+at
       => 0 m/s = 2 m/s - gt = 2m/s - 9.8 m/s^2 * t
       => 2 m/s = 9.8 m/s^2 t
       => t = .204s

12. To calculate how high you are when you stop rising, use the formula
for displacement:   x = x_0 + v_0 t + (1/2) a t^2

where

 x_0 = 0
 v_0 = 2 m/s
 t = 0.204 s
 a = -g = -9.8 m/s^2

Solving the equation for x yields a height of  .20 m.
 
 

Assignment 2. Due Thursday, February 11, 1999

Finish Reading Chapter 1

Do the following exercises from the book on page 33&34:

1, 8, 12, 19, 22, 28, 29 ,31

Do the following problems from the book on page 34:

1, 4, 7, 11

Do the following exercises from the book on page 50:
1,  2, 12, 13
 

Solutions to assignment 2.

Page 33,34

1. Both the floor and the barbell experience their weights.  The floor exerts a large upward force on the barbell and the barbell exerts an equal but opposite downward force on the floor.

8. Both times: Pulling it in and reeling it out both require exerting a force over a distance.

12. 0, Newton’s law: If speed is constant, net force equals zero.

19. 850N in the opposite direction

22. Both pulling and pushing the saw requires work.

28. Gravity.  The hill causes some of the skater’s weight to oppose their motion by acting in the direction opposite to the direction of motion.

29. Transferred into gravitational potential energy you get from attaining a height above the Earth’s surface.

31. Stamping causes your foot and the snow on it to accelerate, when you rapidly change the direction your foot is accelerating, the snow keeps accelerating the original direction and flies off your foot.

Page 34.

1. Since the ramp moves you up 1m for every 20m traveled, it cuts the force required by a factor of (1/20).  The weight of the brick is 20,000kg*9.8=196,000N.  196,000N*(1/20) = 9,800N

4. Potential Energy = (1000kg)(200m)(9.8m/ss) = 196,000J

7. Work = Force * Distance
    25N*.5m = 12.5J

11. Gravitational PE = Mass * Height *Acceleration of Gravity
     (380m)(60kg)(1.6m/ss)=36,480J

Page 50.

1. Torque = Force at a distance from the axis of rotation.  Here there is no distance from the axis so there is no torque.

2. Torque is generated by a force applied perpendicular to the to the radius of rotation.  When you apply the force directly along the axis there is no force perpendicular to the radius of rotation and consequently no torque produced.

12. Same as the example in class with the scissors and the chalk: At the back
of the jaw the teeth are closer to the axis and consequently there is more force being applied through a shorter distance resulting in more crushing power.

13.  Weight on the unbraced shelf will generate a torque causing the board to collapse downward against the wall.  Bracing the board provides a torque to oppose the torque generated by the weight of objects on the shelf.
 

Assignment 3. Due Thursday, February 18, 1999

Look over cases on Pages 72-76 at the end of Chapter 1

Do the following problems from the book on page 50:

1, 2, 5, 9

Do the following exercises from the book on page 70 & 71:

1, 4, 7, 9, 14, 24

Do the following problems from the book on page 71:
1,  5, 6, 9, 10

Solutions for Homework 3
Problems, p. 51

1.  Torque = Force * lever arm = 700 N * 0.175 m = 122.5 N/m

2.  Here, the torque is zero, because the force has no component that is
at right angles to the lever arm.

5.  Torque = Rotational Inertia * Angular Acceleration = I*alpha.  To
increase the angular acceleration by a factor of three, we must also
increase the torque by a factor of three.

9.  The torque is the same at both points, but the forces are different
because they are exerted at different distances from the pivot.

Let r be the distance from the pivot to the nut.  I am using "T" for
torque.

Let F1 be the force of your hand on the end of the nutcracker (F1 = 20 N).
Let F2 be the force of the nutcracker on the nut.

Then,

  T = 5r*F1 = r*F2.

Cancel the r's.  Then,

  F2 = 5*F1 = 5*20 N = 100 N.

The interesting thing about this problem is that we don't need to know the
distance r to find F2.

____________________________________________________________

Exercises, p. 70

1.  Angular momentum.  Since there is no net torque acting on the wheel,
and very little friction, the wheel will keep spinning for a long time.

4.  For the same reason an air bag helps during a car crash.  The leaves
increase the amount of time over which your velocity goes to zero.  You
can think of it like this:

Change in momentum = force * time = mass * change in velocity = constant

So if the time over which the force is applied is increased, the force
required to stop you will be less at any given time.

7.  The skier uses his kinetic energy to do work against sliding friction,
which creates heat.

9.  The rolling pin experiences *static* friction, like a wheel.

14.  The sprinter has to do work against sliding friction, and the
transferred energy becomes heat.

24.  L = I*angular velocity must be conserved.  I is greater when mass is
further from the center of the Earth.  So, when snow melts and the water
runs down the mountains, I decreases.  Therefore, to keep L constant, the
angular velocity must increase.

________________________________________________________
 

Problems, p. 71

(I will use w instead of omega to represent the angular velocity, and T
instead of tau for torque).

1.  K = (1/2) I*w^2
 Let I' = 5*I.
 Let w' = w'/5.

 Then, K' = (1/2)*(I')*(w')^2 = (1/2)*(5I)*(w/5)^2 = (1/2)I*w^2/5
     = K/5.
 Therefore, K' = K/5.

 *Note* A lot of people weren't quite sure what notation to use and
 gave answers like "K = 1/5."  I hope this solution helps a little.
 

5.  p = m*v = (800 kg)*(3 m/s) = 2400 kg m/s forward.

6.  Impulse = change in momentum

 Ft = p
 => t = p/F
      = (2400 kg m/s)/200 N  = 12 s
 (we calculated p in problem 5).

 *Note* Lots of people used F = ma.  That works, too.  This is
 easier.

9.  Momentum is conserved, so 450 kg m/s right.

10.  p = mv = (6 kg)*(5 m/s) = 30 kg m/s.
 

Assignment 4. Due Thursday, February 25, 1999

Answer the following questions from the book on page 261:

1, 2, 5, 7, 9

Do the following exercises from the book on page 262:

4, 7, 9, 10, 19, 21, 22

Solutions for Homework 4.

Solutions for Homework IV

Page261

1. Chemical energy stored in the stick gets transferred into thermal energy (heat).
2. These atoms are held together in the sense that it takes energy to separate them, to move them away from each other.

5. The paper represents a stable configuration of atoms bonded together.  To release the potential in these bonds requires a chemical reaction (burning).  Starting this reaction, however, requires a certain amount of energy called activation energy.  If you light a piece of paper with a match, the lit match is supplying the activation energy.

7. Heat itself does not rise only the heated fluid rises.  Fluids change density when heated and it is this change in density that causes heated air to rise.

9. Conduction, convection and radiation are all mechanism which transfer heat without transferring atoms of molecules.

Page 262

4. The foil reflects the radiated thermal energy from the heating element which is on one side and absorbs heat through conduction evenly across the foil’s surface.  This in turn distributes the thermal energy to the food more evenly.

7. The fire sets up a convection current in the air in the fireplace.  If the wood is raised above the ground air can be more easily supplied to the fire from underneath.  If the fire is well supplied with air it will burn better.

9. A blackened one will absorb more thermal radiation than a shiny one. The shiny one will reflect thermal radiation.

10. Radiation.  Thermal energy can radiate through space.  Heat from the sun is transferred to Earth through radiation. The shuttle has radiators in the cargo bay.

19. The jets in the whirlpool move the water around much faster than before causing the heated water to be circulated, replacing water that had cooled down next to your skin with hotter water.

21. This an example of convection.  Air heated by the Earth rises and gets carried out over the water where it cools and consequently sinks. This cool air is then drawn back toward the warmer land resulting in a strong land breeze.

22.  Because warm air rises, any warmer air in the refrigerator compartment will rise.  If the freezer is place at the top, all the rising warmer air will be cooled when it rises to the top.  If the freezer were at the bottom, warmer air could settle at the top causing a temperature gradient within the refrigerator.  This sets up a convection current.
 

Assignment 5. Due Thursday, March 4, 1999

Do the following exercises from the book on page 274:
1, 2, 4, 6, 8

Do the following problems from the book on page 274:
1,  3

Do the following exercises from the book on page 282:
1, 2, 10, 16

Do the following exercises from the book on page 290:
1, 5, 9

Also Read and Study the cases on pages 291 - 292.
 

Assignment 6. Due Tuesday, March 16, 1999

Read Chapter 7

Answer the following Questions on pages 303-304:
3, 6, 8, 11
Do the following exercises from the book on page 304:
2, 3, 6, 9, 11, 12, 14

Assignment 7. Due Tuesday, March 30, 1999
Answer the following Questions on pages 316:
1, 3, 4, 7, 9, 10
Do the following exercises from the book on page 316:
5, 11, 12, 15, 16
Also Read and Study the cases on pages 316-317.