Dr. Mills 8 Dec 20??

Answer at least 6 of the following questions for full credit on this exam. Show all your work. Circle the answer to each part of each problem you work. Each problem is worth 20 points unless otherwise noted. Work an additional problem as an extra-credit problem for an additional 20 points.

1.  A block of unknown mass is attached to a spring with constant 6.5 N/m and undergoes simple harmonic motion with amplitude 10 cm. When the mass is 1/2 way between its equilibrium position and end point, its speed is 30.0 cm/s. Calculate (a) the mass of the block, (b) the period of the motion, (c) the frequency of the motion, (d) the maximum acceleration of the block. (e) Write an equation describing the displacement of the mass assuming that at time t=0s, the block is released from rest at its lowest position. (12/10+)

2. Consider a 2.0 kg mass attached to a spring driven by an external force F = (3.00 N) cos(2pt). If the spring constant is 20 N/m, determine (a) the period, (b) the amplitude. Assume that there is no damping. (12/31)
3. An astronaut on the Moon wishes to measure the local value of the free fall acceleration, g_Moon, by timing pulses traveling down a wire that has a large mass suspended from it. Assume a wire of mass 4.0 g is 1.6 m long and has a 3.00 kg mass suspended from it. A pulse requires 36.1 ms to travel the length of the wire. Calculate g_Moon using these data. (13/19)
4. A stone is dropped into a deep canyon and is heard to strike the bottom 10.2 s after release. (a) How deep is the canyon? (b) What would be the percentage error in the depth if the time required for the sound to reach the canyon rim were ignored? (13/40)
5. A wave pulse traveling along a string of linear mass density is described by y = A_o e^-bxsin(kx-wt) (a) What is the power P(x) carried by this wave at a point x? (b) What is the power P(0) carried by this wave at the origin (x=0)? (c) Compute the ratio P(x)/P(0). (13/46)
6. A shower stall measures 86.0 cm x 86.0 cm x 210 cm. When you sing in the shower, which frequencies will sound the richest (resonate), assuming the shower acts as a pipe closed at both ends? Assume the range of the human voice extends from 130 Hz to 2000 Hz. Let the speed of sound in the hot shower stall be 355 m/s (use 340 m/s if you take a lot of cold showers) (14/27)
7. A balloon of mass 0.012 kg is filled with helium to a diameter of 1 m. A very light string is tied to the balloon and the balloon is allowed to rise up wile you hold the string. What is the tension on the string? (15/ - )
8. A frog in a hemispherical pod finds that he just floats without sinking in a fluid of density 1.35 g/cm³ If the pod has a radius 6.0 cm and mass of 5 g. What is the weight of the frog? (15/18+)

Quantities you may need to use on this test – if you need others ask me!!