An ancient club is found that contains 150 g of pure carbon and has an activity of 5.5 decays per second. Determine its age assuming that in living trees the ratio of 14C/12C atoms is about 1.00 x 10^-12 . Note that the half life of carbon-14 is 5700 years and the Avogadro number is 6.02 x 10^23 .

A helicopter has two blades (see figure), each of which has a mass of 220 kg and can be approximated as a thin rod of length 6.7 m. The blades are rotating at an angular speed of 43 rad/s. (a) What is the total moment of inertia of the two blades about the axis of rotation? (a) Determine the rotational kinetic energy of the spinning blades.

Problem 1. In the distant future, a physics student is rushing to her final exam traveling in a spaceship at relativistic speed. She passes a policeman at rest a distance 9 km from a traffic signal (measured in his rest frame).

a) The policeman monitors the student’s tail lights (red light with λ=650 nm in her rest frame) with a spectroscope, viewing directly along her motion away from him. He observes a wavelength λ=1300 nm (infrared). What is her speed relative to the policeman?

b) How long, according to her, does it take to reach the traffic signal?

c) When the policeman stops her for running a red light she claims that she saw the traffic signal as green (i.e., λ=520 nm). Compute the wavelength she would have seen. Is she telling the truth?

20. Energy in waves. As a sine-shaped wave moves along a stretched string, each coil os the spring will execute the simple harmonic motion. Suppose that a spring with linear density µ= 0.40 kg/m has a tension T=1.6N in it and that a sine-shaped wave of amplitude 10cm and wavelength of 1.5 is moving along the sprig. Consider a 1cm segment of the spring.

a. What is the mass of the 1cm segment of the spring?

b. What is the speed of the wave along the spring?

c. What is the period of the simple harmonic motion executed by this segment of the spring?

d. Knowing the mass of the segment and the period of its simple harmonic motion, find the effective spring constant of the coil spring for transverse displacements away from its equilibrium.

e. What is the total energy of the simple harmonic oscillator of the segment?

f. There are 150 1cm segments within the 1.5-meter wavelength. What will be the total harmonic oscillation energy in one wavelength of the wave?

g. At what rate in joules/seconds (or with what power in watts) will this energy be transferred past a given point on the spring?

Compare and contrast the following pairs of rocks and explain what is the same and different, and why.

(a) Granite and Rhyolite

(b) Rhyolite and Basalt

(c) Granite and granitic gneiss

(d) Limestone and marble

An electron with a speed of 7.61 × 10⁸ cm/s in the positive direction of an x axis enters an electric field of magnitude 1.14 × 10³ N/C, traveling along a field line in the direction that retards its motion. (a) How far will the electron travel in the field before stopping momentarily, and (b) how much time will have elapsed? (c) If the region containing the electric field is 7.36 mm long (too short for the electron to stop within it), what fraction of the electron’s initial kinetic energy will be lost in that region?

A 500-loop circular armature coil with a diameter of 6.0 cm rotates at 190 rev/s in a uniform magnetic field of strength 0.60 T . What is the rms voltage output of the generator?

What would you do to the rotation frequency in order to double the rms voltage output?

A parallel plate capacitor with a plate area of 2.00cm^2, separated by a distance of 2.00mm is connected to a power supply with a potential difference of 240V. Find the capacitance and charge on each plate.

A cube of side s = 2m sits 1 meter from the origin along the y-axis, as shown. An electric field E = Eo(1+ y/s) j passes through the cube, where Eo = 100 N/C. The charge enclosed in the cube is

a) 6.20 nC

b) 5.31 nC

c) 4.43 nC

d) 3.54 nC

e) 0.00 nC

10) A shower pipe at the beach that is 10 cm in diameter carries water (density 1000 kg/m3 ) up a height of 2.0 m, at which point the pipe narrows to 5 cm and continues another 0.50 m up before the water squires out of the pipe 2.5 m above where it started. Ignore viscosity.

a) If the water moves at 1.5 m/s in the wider part of the pipe, what is its speed in the narrower part of the pipe?

b) What is the pressure change from the bottom of the pipe to the top?

c) What was the pressure of the water at the bottom of the pipe? (Hint: What does the pressure have to be when the water leaves the pipe and is exposed to the atmosphere?)

5. A hollow sphere, a solid cylinder, and a hollow cylinder are all released from rest at the top of a ramp. Which object reaches the bottom of the ramp first?

   (a) The hollow sphere (b) The solid cylinder

   (c) The hollow cylinder
   (d) They all reach the bottom of the ramp at the same time

6. A hollow sphere, a solid cylinder, and a hollow cylinder are all released from rest at the top of a ramp. Which object has the greatest speed at the bottom of the ramp?

   (a) The hollow sphere (b) The solid cylinder

   (c) The hollow cylinder
   (d) They all reach the bottom of the ramp at the same time

7. What is the formula for the moment of inertia of a hollow cylinder rotating about an axis at its edge?

   (a) I = 12MR2 (b) I = MR2

   (c) I = 32MR2 (d) I = 2MR2

8. A meter stick is held such that it rotates at its end. If the meter stick has a mass of 100g, how much torque does gravity produce?

   (a) 0 Nm (b) 0.5 Nm

   (c) 0.75 Nm (d) 1 Nm

Two speakers that are 16.0m apart produce sound waves of frequency 270Hz in a room where the speed of sound is 340m/s . A woman starts out at the midpoint between the two speakers. The room

An interference pattern is produced by light with a wavelength 600 nm from a distant source incident on two identical parallel slits separated by a distance (between centers) of 0.560 mm .

If the slits are very narrow, what would be the angular position of the first-order, two-slit, interference maxima?

What would be the angular position of the second-order, two-slit, interference maxima in this case?

Let the slits have a width 0.280 mm . In terms of the intensity I0 at the center of the central maximum, what is the intensity at the angular position of θ1?