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 115oF, and on some cold winter days it can get as cold as -20oF. 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 cm3when heated from 100oC to 151oC?
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 4oC. If it took a heat 600 seconds to heat this up to 6oC, what is the power rating of the heater?
14. A 95g cup of tea at 85oC is poured into a 1.25 L large tub of water at 30oC . What is the equilibrium temperature?
15. 150 g of ice at -10.5oC is raised to the melting point and then raised to 76.0oC. How much heat is added to the system?
16. A distant star is 7000 K and radiates 1.20 x1027W. What is the star’s radius? Assume ? = 1.0.