You can easily convert common units and measures electronically, but you still should be able to use a conversion table, such as those in Appendix D. Table 1-6 (below) is part of a conversion table for a system of volume measures once common in Spain; a volume of 1 fanega is equivalent to 55.501 dm³ (cubic decimeters).

(a) Complete this table.

	cahiz	fanega	cuartilla	almude	medio
1 cahiz =	1	12	48	144	288
1 fanega =	Enter a number. 1	1	4	12	24
1 cuartilla =	Enter a number. 2	Enter a number. 3	1	3	6
1 almude =	Enter a number. 4	Enter a number. 5	Enter a number. 6	1	2
1 medio =	Enter a number. 7	Enter a number. 8	Enter a number. 9	Enter a number. 10	1

(b) Express 8.00 almude in terms of medio.

Enter a number.

11 medio
(c) Express this in cahiz.

Enter a number.

12 cahiz
(d) Express this in cubic centimeters (cm³).

Enter a number.

13 cm³

The two vectors a and b in Figure 3-29 have equal magnitudes of 14.0 m and their angles are ₁ = 30° and ₂ = 95°.

Figure 3-29

(a) Find the x and y components of their vector sum r.

Enter a number.

1 i +

Enter a number.

2 j
(b) Find the magnitude of r.

Enter a number.

3 m
(c) Find the angle r makes with the positive x axis.

Enter a number.

4°

A particle moves so that its position (in meters) as a function of time (in seconds) is r = i + 6t² j + 7t k.

(a) Write an expression for its velocity as a function of time. (Answer in terms of i, j, k, and t.)

Enter a mathematical expression.

1 m/s
(b) Write an expression for its acceleration as a function of time.

Enter a mathematical expression.

2 m/s²

Four uniform spheres, with masses m_A = 200 kg, m_B = 700 kg, m_C = 1900 kg, and m_D = 400 kg, have (x, y) coordinates of (0, 50 cm), (0, 0), (-80 cm, 0), and (40 cm, 0), respectively. Sphere A is then removed.

(a) Calculate the gravitational potential energy of the remaining three-particle system.

Enter a number.

1 J
(b) Which of the following statements are true? (Select all that apply.)

2

The potential energy of the system increases when A is removed. The potential energy of the system decreases when A is removed. The potential energy of the system does not change when A is removed. The work done by you to remove A is positive. The work done by you to remove A is negative. No work is required to remove A. The work done by you to replace A is positive. The work done by you to replace A is negative. No work is required to replace A.

Mass on a Spring

After running the simulation press the Reset button to activate the sliders. To get the total energy graph to display correctly after changing the initial velocity, hit the Reset button again.

First experiment with the simulation to see what effect changing the initial velocity and the mass has on the motion. Then consider the following four cases, which differ in the settings used in the simulation above:

Case A: Initial velocity = +v; Mass = m
Case B: Initial velocity = -v; Mass = m
Case C: Initial velocity = 0; Mass = m
Case D: Initial velocity = +2v; Mass = m

Predict the results of the questions below, and then use the simulation to verify your predictions.

(a) Rank these cases based on the oscillation amplitude, from largest to smallest (use the notation > or =, for example A>B=D>C).

1

(b) Rank these cases based on the time (after t=0) the mass first passes through the equilibrium position, from longest time to shortest time (use the notation > or =, for example A>B=D>C).

2

Collisions in One Dimension

In the simulation above Ball 1 has a mass M and Ball 2 has a mass nM, where n is an integer. Ball 1 has an initial velocity of v and ball 2 has an initial velocity of -v. Two collisions are carried out with these same initial conditions.

First, the balls undergo a completely inelastic collision (elasticity = 0) where the velocity of both balls after the collision is -0.600 v.

(a) What is the value of n, the ratio of the mass of ball 2 to the mass of ball 1?

1

The same initial conditions are set up but this time the collision is elastic (elasticity = 1). The total kinetic energy both before and after the collision is 137.50 J and the total momentum both before and after the collision is -33.00 kg m/s.

(b) What is M, the mass of ball 1?

2 kg

(c) What is v, the speed of ball 1 before the collision?

3 m/s

AC Circuit with only One Circuit Element

(a) Given the limits on the sliders available to you in the simulation, what are the maximum and minimum values of the "Maximum current" that can be obtained in the simulation?

The maximum possible "Maximum current" is

Enter a number.

1 A.

The minimum possible "Maximum current" is

Enter a number.

2 A.

(b) Which of the following will always result in increasing the "Maximum current" value in an AC Circuit with only one circuit element? Select all that apply.

(c) You have either a resistor, a capacitor, or an inductor connected to an AC source. As you increase the frequency of the voltage you notice that the maximum current increases linearly with frequency. What, if anything, can you conclude about what you have connected to your AC source?

Figure 5-63 shows a box of dirty money (mass m₁) on a frictionless plane inclined at angle ₁. The box is connected via a cord of negligible mass to a box of laundered money (mass m₂) on a frictionless plane inclined at angle ₂. The pulley is frictionless and has negligible mass. What is the tension in the cord? (Answer using m_1 for m₁, m_2 for m₂, theta_1 for ₁, theta_2 for ₂, and g for the acceleration due to gravity.)
T =

Enter a mathematical expression.

1

Fig. 5-63

Figure 11-49 is an overhead view of a thin uniform rod of length L and mass M rotating horizontally at rad/s counterclockwise about an axis through its center. A particle of mass m and traveling at speed v hits the rod and sticks. The particle's path is perpendicular to the rod at the instant of the hit, at a distance d from the rod's center.

Figure 11-49

(a) At what value of d are rod and particle stationary after the hit? (Answer using omega for , and M, m, L, and v, as appropriate.)
d =

Enter a mathematical expression.

1

(b) In which direction do the rod and particle rotate if d is greater than this value?

2

counterclockwise clockwise    

A particle executes linear SHM with frequency 0.35 Hz about the point x = 0. At t = 0, it has displacement x = 0.37 cm and zero velocity. Determine the following values for the motion. Use t for the time as appropriate.

(a) the period

Enter a number.

1 s
(b) the angular frequency

Enter a number.

2 rad/s
(c) the amplitude

Enter a number.

3 cm

(d) the displacement x(t), using t for the time in seconds but not including any units
x(t) =

Enter a mathematical expression.

4 cm

(e) the velocity at time t, using t for the time in seconds but not including any units
v(t) =

Enter a mathematical expression.

5 cm/s


(f) the maximum speed

Enter a number.

6 cm/s
(g) the magnitude of the maximum acceleration

Enter a number.

7 cm/s²
(h) the displacement at t = 3.0 s

Enter a number.

8 cm
(i) the speed at t = 3.0 s

Enter a number.

9 cm/s

Figure 25-44 shows a parallel-plate capacitor of plate area A and plate separation 2d. The left half of the gap is filled with material of dielectric constant ₁; the top of the right half is filled with material of dielectric constant ₂; the bottom of the right half is filled with material of dielectric constant ₃. What is the capacitance? (Answer using A, d, epsilon_0 for ₀, and kappa_1, kappa_2, and kappa_3 for ₁, ₂, and ₃.)
C₁₂₃ =

Enter a mathematical expression.

1

Figure 25-44

Switch S in Fig. 30-63 is closed at time t = 0, initiating the buildup of current in the inductor of inductance L and the resistor of resistance R. At what time is the emf across the inductor equal to the potential difference across the resistor? (Answer using L and R, as appropriate.)
t =

Enter a mathematical expression.

1

Fig. 30-63

In Figure 33-79, unpolarized light is sent into a system of three polarizing sheets with polarizing directions at angles ₁, ₂, and ₃. What fraction of the initial light intensity emerges from the system? (Answer using for theta_1, theta_2, and theta_3 for ₁, ₂, and ₃, respectively.)
I =

Enter a mathematical expression.

1

Fig. 33-79