Question 2

A mass attached to a spring oscillates with a period of 2.00 s. If the mass starts from rest at x = 4.50 x 10^-2m and time t= 0, where is it at time t = 8.80 s? Express your answer in centimeters.

Plug in the respective values in Eq. (13-4).

Question 3

When a 0.184-kgmass is attached to a vertical spring, it causes the spring to stretch a distanced. If the mass is now displaced slightly from equilibrium, it is found to make 49 oscillations in 6.4s. Calculate distancedin centimeters.

Use the definition of period (the beginning of section 13-1) to calculate the period.

Use the period and the mass to calculate the spring constant from Eq. 13-11.

Use Hooke's Law to find d (the first equation in section 13-4, also in section 6-2). Do not submit a negative value. The negative sign of this equation (page 430) indicates that the direction of the force is opposite to the direction of the deformation. All these quantities are positive however.

Question 4

A simple pendulum of length 2.40 mmakes 4.0 complete swings in 35.6s. What is the acceleration of gravity at the location of the pendulum?

Again, use the definition of period to calculate the period (the beginning of section 13-1).

Once you have the period, use Eq. 13-20 to calculate g.

Question 6

A brother and sister try to communicate with a string tied between two tin cans.

If the string is 7.6-mlong, has a mass of 20.0g, and is pulled taut with a tension of 16.5 Nhow much time, in seconds, does it take for a wave to travel from one end of the string to the other? Use three significant figures in your answer.

First, calculate the mass of the string per length, a quantity that is introduced in section 14-2 (p. 460). Make sure it is expressed in kg/m, not in g/m.

Use Eq. 14-2 to find the speed in the string (also Exercise 14-2) since you know and the tension.

Now that you know the speed and the distance, you can find the time; use the definition of average speed (Eq. 2-3).

Question 7

Two steel guitar strings have the same length. String A has a diameter of 0.835mmand is under 530Nof tension. String B has a diameter of 1.40mmand is under a tension of 810.0N. Find the ratio of the wave speeds, v_A/v_B, in these two strings. Use three significant figures in your answer.

Keep in mind that the strings are cylinders. Use the formula mass = density x volume. What is the volume of a cylinder? Then use Eq. 14-2.

You should get this expression:=42, in which F is the tension, is the density and d is the diameter. Feel free to use this formula directly if you are unable to derive it using the information provided above.

Take the ratio of the two speeds. The density will cancel out (same material), so the ratio of the speeds is dictated by the ratio between tensions and the ratio between densities.

Question 8

Two people relaxing on a deck listen to a songbird sing. One person, only 3.40from the bird, hears the sound with an intensity of 1.2010⁵W/m². How far could a second person be from the bird described and still be able to hear it? Express your answer in kilometers, with three significant figures. Remember that the lowest intensity the human year can perceive is 1.010^-12W/m².

Use Eq. 14-7 to calculate the power of the source, P (we know the intensity and the distance).

Then, use the same formula again to calculate r for the second person (now you know I and P).

Question 9

The sound intensity level of an annoying mosquito is 14.0 dB. Calculate the sound intensity level of 26 identical mosquitoes, at the same location, in decibels.

Use Eq. 14-8 to calculate the intensity (I) for one mosquito. Do you remember how to handle logarithms? beta/10 = log(I/I0), I/I0 = 10^(beta/10).

Then, use the same equation again to calculate the intensity level for N mosquitoes (the intensity is N times greater than the value for one mosquito, NI).

Question 10

In the Bohr model, as it is known today, the electron is imagined to move in a circular orbit about a stationary proton. The force responsible for the electron's circular motion is the electric force of attraction between the electron and the proton. If the speed of the electron were 3.9010⁵m/s, what would be the corresponding orbital radius, in nanometers to three significant figures?

The Coulomb force acts as the centripetal force, as shown in Eq. 31-3, in which m is the mass of the electron, e is the charge of the electron/proton, and the value of k is given in Eq. (19-6).

Solve for r and convert your answer to nanometers.

Question 11

What is the magnitude of the electric field produced by a charge of magnitude 7.80Cat a distance of 43.0 cm? Express your answer in kN/C with at least three significant figures.

Use Eq. 19-10 and Example 19-12. Watch for the units!

Question 12

Highly sensitive ammeters can measure currents as small as 13.4fA. How many electrons per second flow through a wire with this current? Do not round your answer ... too much.

Use Eq. 21-1 with the time being equal to 1 second to find the charge.

Then calculate the number of electrons as shown in Example 21-1.

Question 13

When a potential difference of 22.2Vis applied to a given wire, it conducts 0.400Aof current. What is the resistance of the wire, in ohms?

Use Ohm's Law (Eq. 21-2).

Question 14

A current of 2.00Aflows through a copper wire 0.850mmin diameter when it is connected to a potential difference of 13.6V. Calculate the length of the wire, in kilometers to three significant figures. Use the resistivity of copper as given in Table 21-1.

Use Eq. 21-2 to calculate the resistance (R) and then Eq. 21-3 to calculate the length (L).

Question 15

A negatively charged ion moves due north with a speed of v = 1.30 x 10⁶m/s at the Earth's equator. The strength of the magnetic field at that location is 0.048 mT. What is the magnetic force exerted on this ion, in newtons?

Use Eq. 22-1 with the angle being 0 degrees.

Question 17

A wire with a current of 3.80Ais at an angle of 38.0⁰relative to a magnetic field of 0.80T. Find the force exerted on a 3.40mlength of the wire, in newtons.

Use Eq. 22-4.

Question 19

Two long, straight, parallel wires are separated by a distance of 6.50cm. One wire carries a current of 2.75A,the other carries a current of 4.34A in the same direction. Calculate the strength of the magnetic field halfway between the wires, in microteslas.

Use Eq. 22-9 twice to calculate the magnetic field produced by each wire at that location (Exercise 22-13).

Do you add or do you subtract these two quantities? Please refer to Example 22-15.