Final Exam, Physics 170, Fall 1995.
Please write your name at the top of the page. Show your work. There are 8 problems. Each is assigned 25 points. You have two hours to complete the exam.
1. Dimensional Analysis
A length L that appears in atomic physics is given by the formula
where is the mass of an electron, c is the speed of light, and h is a constant known as Planck's constant.
What are the dimensions (or units) of Planck's constant, h ?
2. Conservation Laws: Energy, Momentum and Angular Momentum
An air puck with mass 0.4 kg and velocity on a flat frictionless table collides with a second air puck of mass 0.5 kg and velocity . As a result of the collision, the first puck stops while the second puck starts moving. (hint: remember these velocities are vectors and draw a clear diagram.)
(a) What is the kinetic energy of the system before the collision ?
(b) What is the kinetic energy of the second air puck after the collision ?
3. Static Equilibrium
You have been hired by Paradise Island Engineering. Your job is to design a cable for the arrangement shown below. A uniform beam of length L and mass M is pivoted at one end about an attachment point in a wall. The other end is supported by a horizontal cable also attached to the wall. The beam makes an angle with the horizontal.
(a) Draw a diagram which shows the forces acting on the beam ?
(b) What is the tension in the cable ? (give your result in terms of )
The mass of the moon is kg and its radius is 1740 km ( N-m /kg ).
(a) What is the period of a satellite in a circular orbit 1000 km above the surface ?
(b) What is the escape velocity for a projectile that is fired from the moon's surface ?
5. Oscillatory Motion
A sphere of mass M and radius R is attached to the ceiling (as shown) and allowed to oscillate.
(a) What is the period of small oscillations ? (The momenta of inertia for a sphere about an axis through its center is .)
(b) Suppose the initial amplitude is rad, and the sphere starts at rest. What is , the angular displacement as a function of time ? (give your final result in terms of R, g, t).
6. Sound Waves
A organ pipe open at both ends is excited in its third harmonic. The length of the pipe is 0.3 m. The speed of sound in air is 340 m/s.
(a) What is the frequency of the sound produced ?
(b) What is the wavelength of the sound produced ?
(c) Suppose an observer is rapidly moving towards the end of the organ pipe. Will the frequency of the sound heard by the observer be higher or lower than the frequency in part (a) ? (give a short qualitative explanation of your answer).
(d) Suppose an observer is rapidly moving towards the end of the organ pipe. Will the wavelength of the sound found by the observer be higher or lower than the wavelength found in part (b) ? (give a brief qualitative explanation of your reasoning).
7. Kinetic Theory of Gases
The surface of the sun contains both hydrogen and helium atoms at 6000 K.
(a) What is the average kinetic energy for each type of atom ?
(b) What is the rms velocity for each type of atom ?
(c) Which type of gas is most likely to escape from the sun ? (give a brief qualitative explanation for your answer)
(Some of the following information may be useful: J/K, R=8.31 J/mol K, R=0.0082 L-atm/mol K, atoms/mole, the mass of a hydrogen atom is kg. Also note that He has atomic mass 4.)
How much perspiration must evaporate from a large sweaty Hawaiian warrior who weighs 150 kg in order to reduce his temperature by C ? (find the amount of perspiration in kg).
(Some of the following information may be useful: the heat of vaporization for water at room temperature is 580 cal/g. 1 cal=4.184 J, 1 Btu= 252 cal. The latent heat of fusion for water is 79.7 cal/g. For the body, c=0.83 cal/g .)