19. Consider two Carnot engines connected in series. The efficiency for the first engine is ε₁ while the efficiency for the second engine is ε₂. What is the overall efficiency of the combined system?

(A) ε₁ + ε₂
(B) ε₁ε₂
(C) (ε₁ + ε₂)/2
(D)
(E) ε₁ + ε₂ − ε₁ε₂

20. What is the bulk modulus (i.e., inverse compressibility) for a diatomic ideal gas measured from adiabatic compression/expansion? (γ = 1.4 for a diatomic ideal gas; P: pressure; ρ: density; T: temperature) (A) γT/P (B) γP/ρ (C) γP (D) P (E) none of the above.

1. In the figure, a uniform rectangular crate 0.40 m wide and 1.0 m tall rests on a horizontal surface. The crate weighs 1000 N, and its center of gravity is at its geometric center. A horizontal force F is applied at a distance h above the floor. If h = 0.8 m, what minimum value of F is required to make the crate start to tip over? (Static friction is large enough that the crate does not start to slide.) (A) 500 N(B) 750 N(C) 250 N(D) 625 N(E) 1000 N

2. A record is dropped vertically onto a freely rotating turntable (kinetic energy of the record is negligible). Frictional forces act to bring the record and turntable to a common angular speed. If the rotational inertia of the record is 0.66 times that of the turntable, what percentage of the initial kinetic energy is lost?(A) 40%(B) 34%(C) 56%(D) 66%(E) 19%

3. A 15-g bullet is shot vertically into a 2-kg block. The block lifts upward 8.0 mm. The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The kinetic energy of the bullet lost in the block is closest to (A) 14 J(B) 21 J(C) 0.16 J(D) 0.0012 J(E) 10 J

4. A satellite is in circular orbit at an altitude of 2300 km above the surface of a nonrotating asteroid with an orbital speed of 5.9 km/s. The minimum speed needed to escape from the surface of the asteroid is 14.6 km/s. The mass of the asteroid is closest to(A) 3.0 × 10²⁴ kg(B) 9.0 × 10²³ kg(C) 1.0 × 10²⁴ kg(D) 2.0 × 10²⁴ kg(E) 4.0 × 10²⁴ kg

5. Is it possible for a system to have negative potential energy?(A) No, because this would have no physical meaning.(B) No, because the kinetic energy of a system must equal its potential energy.(C) Yes, as long as the kinetic energy is positive.(D) Yes, as long as the total energy is positive.(E) Yes, since the choice of the zero of potential energy is arbitrary.

6. An experimental rocket sits on its launching pad on earth pointing vertically upwards. Its total mass is 7×10⁶kg, of which 6.5 × 10⁶ kg is fuel. Its engines shoot exhaust downward at a rate of 2000 kg/s with a speed of 3000 m/s relative to the rocket. Calculate the approximate delay between ignition and lift off.(A) It never lifts off.(B) 53 minutes(C) 27 minutes(D) 1 minutes(E) No delay

7. A 2.0 kg block on a frictionless table is connected to two ideal massless springs with spring constants k₁ and k₂ whose opposite ends are fixed to walls, as shown in the figure. What is angular frequency of the oscillation if k₁ = 7.5 N/m and k₂ = 5.0 N/m? (A) 2.5 rad/s(B) 3.5 rad/s(C) 0.40 rad/s(D) 0.56 rad/s(E) 1.2 rad/s

8. Upon being struck by 240-nm photons, a metal ejects electrons with a maximum kinetic energy of 1.45 eV. What is the work function of this metal?(A) 5.18 eV(B) 4.92 eV(C) 4.33 eV(D) 3.73 eV(E) 3.13 eV

9. In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density 1000 kg/m³) that is 3.0 m thick. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be 5.0 × 10⁴ Pa? The density of the oil is 510 kg/m³. (A) 9.2 m(B) 8.2 m(C) 4.1 m(D) 2.0 m(E) 1.2 m

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