Final Exam. Useful tables. 1 : [10 pts] 2 : [10 pts] 3 : [10 pts] 4 : [10 pts] 5 : [10 pts] 6 : [10 pts] 7 : [10 pts] 8 : [10 pts] TOTAL:

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1 Final Exam Name Score Please PRINT your name. Read the question carefully. Show your steps. Use letter symbols first if convenient. Give units on final answers. Diagrams help. Do all work on these pages, referring to back side if necessary. Do not communicate with others. SI-units are used. Useful tables Specific Heats Substance Specific heat [J/kg/K] Elemental Solids Lead 128 Tungsten 134 Silver 236 Copper 386 Aluminum 900 Other Solids Brass 380 Granite 790 Glass 840 Ice ( 10 C) 2220 Liquids Mercury 140 Ethyl alcohol 2430 Seawater 3900 Water : [10 pts] 2 : [10 pts] 3 : [10 pts] 4 : [10 pts] 5 : [10 pts] 6 : [10 pts] 7 : [10 pts] 8 : [10 pts] TOTAL:

2 Useful relations g = 9.80 x x 0 = v 0 t at2 v = v 0 + at 2(x x 0 ) = (v + v 0 )t 2a(x x 0 ) = v 2 v 2 0 v P A = v P B + v BA F = ma w = mg F = kx fs µ s n f k = µ k n K = 1 2 mv2 W = F s = F s cos φ K = W net W g = mg y W s = 1 2 kx2 i 1 2 kx2 f P = W/ t 1 hp = 746 P = F v U = mgy U = 1 2 kx2 F = U (K + U) = W nc p = mv F = p/ t I = F t I = p f p i Mr cm = i m i r i P = Mv cm = i m i v i Fext = Ma cm Fext = P/ t P i = P f v 3 = [(m 1 m 2 )v 1 + 2m 2 v 2 ]/(m 1 + m 2 ) v 4 = [2m 1 v 1 + (m 2 m 1 )v 2 ]/(m 1 + m 2 ) θ θ 0 = ω 0 t αt2 ω = ω 0 + αt 2α(θ θ 0 ) = ω 2 ω0 2 2(θ θ 0 ) = (ω + ω 0 )t s = θr v = ωr a tan = αr a = v 2 /r T = 2πr/v I = i m i ri 2 I = 1 12 ML2 I = 1 3 ML2 I = 1 12 M(a2 + b 2 ) I = 1 3 Ma2 I = 1 2 MR2 I = MR 2 I = 2 5 MR2 I = 2 3 MR2 I = I cm + Md 2 K = 1 2 Iω2 τ = F l τ = r F τext = Iα W = τ θ L = r p L = Iω τ ext = L/ t F/A = E L/L p = B V/V F/A = G x/l F = Gm 1 m 2 /r 2 U = GmM/r p = p 0 + ρgh Q = V/ t = Av = const. p + ρgy ρv2 = const. B = ρ F V g Q = πr 4 p/(8ηl) L = αl 0 T V = βv 0 T Q = mc T Q = ±ml H = ka(t 2 T 1 )/L pv = nrt = Nk B T W = p V E tr = 3 nrt = 3 kt v 2 rms = 3k B T/m = 3RT/M C V = f R C 2 P = C V + R U = Q W pv γ = const. T V γ 1 = const. U = nc V T γ = C p /C V W = (p i V i p f V f )/(γ 1) e = W/Q h = 1 Q c /Q h e = 1 T c /T h COP = Q c /W COP = Q h /W S = Q/T S = nc V ln T f T i + nr ln V f V i a = ω 2 x E = 1 2 mv mω2 x 2 x = A cos(ωt + φ) ω = k/m ω = g/l ω = mgh/i ω = 2πf = 2π/T y = A sin(kx ωt) v = λf k = 2π/λ v = τ/µ P = µω 2 A 2 v/2 λ = 2L/n I = 2π 2 ρvf 2 A 2 I = P/(4πr 2 ) β = 10 log(i/10 12 ) f = f(v ± v o )/(v v s ) λ = 4L/n

3 Physical Constants Name Symbol Value Unit Number π π Number e e ( n ) Euler s constant γ = lim 1/k ln(n) = n k=1 Elementary charge e C Gravitational constant G, κ m 3 kg 1 s 2 Fine-structure constant α = e 2 /2hcε 0 1/137 Speed of light in vacuum c m/s (def) Permittivity of the vacuum ε F/m Permeability of the vacuum µ 0 4π 10 7 H/m (4πε 0 ) Nm 2 C 2 Planck s constant h Js Dirac s constant h = h/2π Js Bohr magneton µ B = e h/2me Am 2 Bohr radius a Å Rydberg s constant Ry ev Electron Compton wavelength λ Ce = h/m e c m Proton Compton wavelength λ Cp = h/mpc m Reduced mass of the H-atom µ H kg Stefan-Boltzmann s constant σ Wm 2 K 4 Wien s constant k W mk Molar gasconstant R J mol 1 K 1 Avogadro s constant N A mol 1 Boltzmann s constant k = R/N A J/K Electron mass me kg Proton mass mp kg Neutron mass mn kg Elementary mass unit mu = 1 12 m(12 6 C) kg Nuclear magneton µ N J/T Diameter of the Sun D m Mass of the Sun M kg Rotational period of the Sun T days Radius of Earth R A m Mass of Earth M A kg Rotational period of Earth T A hours Earth orbital period Tropical year days Astronomical unit AU m Light year lj m Parsec pc m Hubble constant H (75 ± 25) 1 km s 1 Mpc

4 1. A 120 g insulated aluminum cup at 15.0 C is filled with 140 g of water at 50.0 C. After a few minutes equilibrium is reached. (a) Determine the final temperature. (b) Estimate the total change in entropy.

5 2. If mol of helium is at 10 C and a gauge pressure of atm, calculate (a) the volume of the helium gas under consideration, and (b) the temperature if the gas is compressed to precisely half the volume at a gauge pressure of 1.00 atm.

6 3. Ear trumpets were never very common, but they did aid people with hearing losses by gathering sound over a large area and concentrating it on the smaller area of the eardrum. What decibel increase does an ear trumpet produce if its sound gathering area is 900 cm 2, the area of the eardrum is cm 2, but it only has an efficiency of 5.00% in transmitting the sound to the eardrum?

7 4. A uniform sphere has a radius of 4.2 cm and a mass of 1.3 kg (a) What is the kinetic energy of the sphere if it is spinning at 19 Hz about an axis through its center. (b) Assume we release the sphere from rest at the upper end of the track shown in the figure and it rolls without slipping until it rolls off the right-hand end. If H = 2.0 m and h = 0.70 m and the track is horizontal at the right hand end, determine the distance to the right of the point A at which the ball strikes the horizontal base line. H A. h

8 5. A 530 g block of wood resting on a frictionless table is struck through its center by a 10.0 g bullet moving at 410 m/s. The bullet emerges at the opposite side of the block with a velocity of 180 m/s. (a) What is the velocity of of the block immediately after the bullet has emerged? 410 m/s 180 m/s (b) If the table is not frictionless, and the coefficient of friction between the block and the table is 0.20, how far does the block travel before it gets to a stop?

9 6. Calculate the rate at which body heat flows out through the clothing of a skier, given the following data: the body surface area is 1.8 m 2 and the clothing is 1.2 cm thick; skin surface temperature is 33 C, whereas the outer surface of the clothing is at 1.0 C; the thermal conductivity of the clothing is W/K/m. How would the answer change if, after a fall, the skier s clothes become soaked with water? Assume the thermal conductivity of water is 0.60 W/K/m.

10 7. Jane has a pendulum which consists of a 1.5 kg mass suspended from a point P by a thin rod as shown in the figure. With a horizontal force, Jane first displaces the mass to an initial angle θ 0 = 8.0. Before she releases it, she holds it still at this angle for a moment. (The rod is made out of light weight material, and its mass can be neglected.) P (a) Find the force Jane exerts on the pendulum, while she is holding it still. θ 0 F (b) Jane releases the pendulum exactly at time t = 0, and she finds that it returns to its initial position every 2.6 s. Find the length of the pendulum. (c) What angle does the pendulum make with the vertical 5.8 s after Jane has released it?

11 8. A 2.54 kg block is dropped from a height of 43.6 cm onto a spring of force constant k = 28.8 N/cm, as shown in the figure. Find the maximum distance the spring will be compressed.