Week 6

Please
solve following problems. Show the step
by step process used to reach each solution.

1. A spring with negligible mass stretches 34.0 cm when a 144 g
gram mass is suspended from it. Now I suspend a mass m from the spring. If
it oscillates at an angular frequency of 4.51 rad/s, what is the mass?

2. A 3.45 kg mass vertically compresses a spring 67.0 cm before it
starts to rebound. How high will the Mass move above the uncompressed it
the mass is left to “bounce” back up?

3. A transverse traveling wave on a cord is represented by D =
0.25 sin (6.8x + 28t) where D and x are in meters and t is in seconds.

a) Determine the wavelength of this wave.

b) Determine the frequency of this wave.

c) Determine the speed of this wave.

d) Determine the amplitude of this wave.

f) Determine maximum and minimum speeds of particles of the cord.

4. A person is watching water waves at the ocean and they notice
the peak to peak distance between the waves is 3.4 m. They also notice there
are 55 waves every 10.0 seconds passing the end of a pier. How fast are the
waves going?

5. A whale sends an undersea signal to its mate and then gets a
response 4.5 seconds later. How far away is the whale’s mate?

6. A person sees a distant lightning strike, then 4.5 seconds
later he hears the thunder clap. If it is 35 degrees Celsius, how far away
was the lightning strike?

7. A single bass amplifier produces a volume of 102 dB. What is
the sound level if a guitar amplifier what produces 98 dB is played at the same
time?

8. A string on a guitar vibrates at 420 Hz. If the tension on the
string is 102 N, what is the mass of the string if the portion that
vibrates is 63.7 cm long?

9. A diamond has a mass of 56.6 g and the gold ring it is set in
has a mass of 125.6 g. How many carbon atoms are there compared to gold atoms?

10. On a warm summer day in California it can get as hot as 115^{o}F,
and on some cold winter days it can get as cold as -20^{o}F. What are
these temperatures in Celsius?

11. An aluminum sphere is 5.50 cm in radius. What is its volume
expansion coefficient if it increases in volume 2.00 cm^{3}when heated from 100^{o}C to 151^{o}C?

12. Carbon 12 is defined such that 12g is one mole. So if a
diamond is 37.5 g, how many moles of carbon are in it? How many molecules of
carbon are in it?

13. 400 L of water is at 4^{o}C.
If it took a heat 600 seconds to heat this up to 6^{o}C, what is the power
rating of the heater?

14. A 95g cup of tea at 85^{o}C
is poured into a 1.25 L large tub of water at 30^{o}C . What is the
equilibrium temperature?

15. 150 g of ice at -10.5^{o}C
is raised to the melting point and then raised to 76.0^{o}C. How much heat is added
to the system?

16. A distant star is 7000 K and radiates 1.20 x10^{27}W. What is the star’s radius? Assume ?
= 1.0.