Hints for Physics 170

Assignment I

1-4 : Review Table 1-1
1-6 : Review Section 1-3
1-18 : See example 1-2
1-20 : The argument of the exponential is dimensionless.
1-26 : The dimensions of force are kg m/sec^2. Now follow the procedure in example 1-2
1-52 : What is the volume of a sphere in terms of its radius ? (See appendix D for mathematics review)

Assignment II

2-8 : Review Section 2-1 and definitions of velocity, displacement.
2-15 : Again review Section 2-1 and definitions of velocity, displacement
2-22 : Review examples 2-5 and 2-6 and the graphical interpretation of average and instantaneous velocity
2-24 : Review examples 2-5 and 2-6. Also equations 2-5 and 2-6.
2-36 : Review examples 2-5 and 2-6 and the graphical interpretation of velocity and acceleration
2-40: Review equations 2-5 and 2-10

Assignment III

2-72 : Review applications of equation 2-15. Use v^2= v_0^2 + 2 a delta x. The velocity just after leaving the floor is slightly less than the velocity that it hits the floor since the final height 2m is less than the initial height. For part (c), a reasonable guess is the ball is contact with the floor for 0.05 s.
2-76 : Write down expressions for the velocity and displacement at all times in terms of v_0 and a. Insert the known information and then solve.
2-82: Review examples 2-15 and 2-18. Write expressions for the displacement of each stone and then insert the given information.
2-122 : Review examples 2-15 and 2-18. Write expressions for the displacement of each police car and then insert the given information.
3-14 : Review section 3-2 and equation 3-8.
3-16 : Review section 3-2 and operations with vectors in Table 3-1

Assignment IV

3-36 : Write the vector displacement and velocity in component form. Review examples 3-3 and 3-6
3-38 : Review example 3-5
3-42 : Review example 3-4
3-58 : Write the x and y components of the displacement. What is the y component of the velocity at its highest point ?
3-70 : Find the time of flight first. Review examples 3-8 and 3-9 for similiar problems.
3-102 : Find the condition on the velocity to clear the cars. Remember the motorcyclist can only drop 5 m and that the initial velocity is in the horizontal direction.

Assignment V

4-12 : Add the force vectors. Review example 4-7 if necessary.
4-14 : How are displacement and acceleration related for constant acceleration ?
4-24 : Review the difference between mass and weight, section 4-3.
4-32 : Review section 4-4

Assignment VI

4-42 : Review section 4-6. (b) Static equilibrium implies the net force is zero.
4-47 : Review example 4-9.
4-56 : Balance force components. Review examples 4-8 and 4-9.
4-76 : Define a convenient coordinate system. Then write down the equations of motion in the x and y directions for each mass.
4-81 : Define a convenient coordinate system. Then write down the equations of motion in the x and y directions for each mass. How are the accelerations of mass 1 and mass 2 related ?

Assignment VII

5-4 : What is the acceleration along the inclined plane ?
5-14 : Review example 5-1.
5-22 : Review example 5-4 and example 4-8
5-55 : Write the equation of motion for each block. Be careful about the signs.
5-66 : Review example 5-9.

Assignment VIII

5-34 : Review example 5-6.
5-52 : Review examples 5-8 and 5-9
5-108 : (a) What is the magnitude of r vector ? What is the equation that describes a circle ?
6-6 : Review the definition of kinetic energy.
6-10 : Use the Work-Energy Theorem.
6-20 : Review example 6-8
6-26 : Review p. 155-157

Assignment IX

6-42 : An easy way: Use Power x time = Delta K.E.
6-56 : (a) Review definition of U_grav (b),(c) Use kinematic equations from chapter 3 (d) Use conservation of mechanical energy. energy. Review example 6-12
6-61 : Review Atwood's machine example from class or example 7-5. Express K in terms of m_1 + m_2. Express a in terms of m_1, m_2 and g. Now solve for the masses.
6-78 : The potential energy of N people is N m g h. Compare this to the energy in Joules that corresponds to 54.3 billion kW-h.
7-6 : Define the zero of U_grav at the equilibrium position. Apply conservation of energy as in example 7-2.

Assignment X

7-8 : Conserve mechanical energy. Study example 7-3.
7-18 : Compute the mechanical energy at P and Q. Conserve energy.
7-20 : Conserve mechanical energy. Pick a convenient point for U_grav=0. Then write down E_i and E_f.
7-42 : What is U= m g h. Remember to how express mass in terms of density.
7-49 : Break up into two parts, the sloped and flat sections. For the first part delta E=0. For the second part, delta E= W_nc (the work done by friction).
7-82 : Use conservation of energy and remember the normal force N=0 when the particle has just enough velocity to go around the top of the loop.

Assignment XI

8-6 : Find the center of the mass of the handle. Find the center of mass of the club. Now treat as two point particles located at the center of masses of each.
8-7 : Review definition of center of mass on p 213.
8-18 : Review section 8-3 and use equation 8-7.
8-19 : Review section 8-3.
8-32 : Use conservation of momentum. P_i = ? P_f = ?

Assignment XII

8-66 : Review example 8-17. Use conservation of momentum and energy.
8-69 : (a) Review equation 8-7 (b) After the collision while the masses are connected, energy is conserved. (c) The collision is elastic. (d) Note that this is easiest in the CM frame
8-114 : During the collision, momentum is conserved. After the bullet is embedded, energy is conserved.
8-121 : The net external force is zero since truck and car make an action-reaction pair.

Assignment XIII

9-6 : review section 9-1 and example 9-1
9-23 : Review example 9-6.
9-30 : review definition of moment of inertia and example 9-2
9-33 : Review parallel axis theorem (9-21) and example 9-4
9-48 : (a) Use equation 9-23 (b) review how to calculate the moment of inertia (eqn 9-17)
9-68 : An easy way to do this. First use conservation of mechanical energy to get the velocity v. (Don't forget about the rotational kinetic energy of the wheel). Then find acceleration a from v^2= 2 a delta x. Be careful about the tensions, since the pulley is not masseless T_1 is not quite equal to T_2.

Assignment XIV

9-86 : Study example 9-15.
9-92 : We have done this before. Don't forget to include the rotational kinetic energy.
9-118 : Conservation of energy. Don't forget to include the rotational kinetic energy.
10-4 : Use equation 10-11
10-5 : Review cross product of vectors p 296
10-26 : Torque is r x F and dL/dt. Use both
10-72 : Review definition of angular momentum and example 10-1

Assignment XV

10-34 : If F and r are parallel, what is the torque ?
10-38 : Study example 10-3
10-50 : Review example 10-7
10-82 : Review problem 10-34. Look at Figure 11-4.

Assignment XVI

General hints : Remember that if the r and F vectors are parallel then r x F is zero. For the Kepler's Laws problems, use this to deduce that angular momentum is conserved. For the second Kepler's law problem, remember how to express the area of a triangle in terms of the lengths of the sides.
For angular momentum conservation problems. Write down initial and final angular momenta. Remember that the motion can be decomposed into two parts, motion of the center of mass and motion relative to the center of mass.

Assignment XVII

11-81 : Use the hint in the problem. Write down the gravitational field of the large sphere. Write down the gravitational field of the smaller sphere. Remember their centers are at different locations
11-105 : Write down the force as a function of radius. (It will depend on the mass enclosed at radius r. Review equation 11-27 and accompanying text). Now integrate F dr and use energy conservation
12-16 : The sum of torques is zero. Use this principle as in examples 12-1 and 12-2.
12-28 : Study example 12-3
12-34 : Review example 12-4
12-48 : Review example 12-5. Remember the frictionless floor only exerts a normal force on the ladder. Balance forces and torques.

Assignment XVIII

13-18 : Review buoyant force (examples 13-6, 13-7) and equation 13-13
13-12 : Review Pascal's principle
13-26 : Think about Archimedes principle and the size of the buoyant forces.
13-51 : Similiar to example 13-8. An application of Bernoulli's Law.

Assignment XIX

14-6 : Review examples 14-1 and 14-2
14-18 : Review p. 409 and homework problem 5-108
14-46 : Review section 14-3
14-58 : Review the physical pendulum. Use the parallel axis theorem, p. 265.
14-116 : Use the hint in the text i.e write F= k_eff * x and solve for k_eff.

Assignment XX

14-76 : Review section 14-4 and example 14-12
14-90 : Review example 14-13. After one cycle, E= E_0 * (1- Delta E/E). After n cycles, E = E_0 * (1- Delta E/E)^n
15-8: What is the relation between tension, linear density and wave speed ?
15-28: Review example 15-4. Note f(x-v t) (f(x+v t)) describes a wave traveling to the right (left).
15-36: Use equation 15-22
15-40: How does spherical wave intensity fall off with distance. Review section 15-3.

Assignment XXI

15-44 : Review the definition of the decibel scale p. 457
15-68 : Does lambda (wavelength) change in this case ?
15-60 : Try to draw a picture of the wavefronts.
15-101 : Review p 443 and example 15-4
16-12 : Review examples 16-2 and 16-3.
16-46 : Review p. 493
16-49 : Review section 16-2

Assignment XXII

16-8 : Use equation 16-9 to find the phase difference. Use equation 16-6 to find the amplitude. (Review examples 16-2 and 16-3)
16-76 : Review the string fixed at one end p. 492
18-24 : Use equation 18-13. Be careful to use R with the correct units. (Review example 18-3)
18-32 : Remember P = P_0 + rho g h (chapter on fluids). Now use P V = n R T. Be careful with units.
18-40 : Reread p 551 (careful about the units of R)
18-44 : Review example 18-7. Read the paragraph on p 558 below the example.
18-62 : Review p 550

Assignment XXIII

19-2 : review p 567
19-6 : Review examples 19-3 and 19-4 (remember you must take into account the energies associated with phase changes as well as the energy to raise/lower the temperature)
19-10 : Review example 19-5
19-12 : No phase changes. The two substances must come into equilibrium and be at the same final temperature. The heat lost by the lead is equal to the heat gained by the water.
19-28 : Review equation 19-10 and example 19-6
19-40 : Review section 19-5 and example 19-7

Assignment XXIV

19-20 : Calculate the heat flow for each component. Set the sum equal to zero. Review example 19-4.
19-38 : Review the discussion of PV diagrams p. 576-577
19-54 : What is the internal energy for a diatomic gas ? (see p. 582) (b) Find dT first, now determine d U, and get W from the first law of thermodynamics (c) How much work is done if the volume is held constant ? Note example 19-9 is similiar
20-6 : Use equation 20-2. See example 20-1.
20-52 : Review of concepts in chapter 20

Tom Browder
December 3, 1998