10. A particle experiences a force given by F(x) = α - βx³. Find the potential energy U(x) of the particle.
(Assume that the zero of potential energy is located at x = 0.)
(A)
(B)
(C) U(x) = 3βx²
(D) U(x) = -3βx²
(E) U(x) = -6βx

6. A 2 kg object is subjected to three forces that give it an acceleration = (−8 m  ⁄s2 )+(6 m/s2) . ff two of the three forces are and ,find the third force.(A) (B) (C)(D) (E)

7. n moles of gas in a container of volume at temperature T expands rapidly into an evacuatedregion after a membrane is broken. The final volume of the gas-occupied space is . What is thechange in thermal energy? (The universal gas constant is R.)(A) (B) (C)(D) (E)

8. A medical defibrillator stores 320 J in a 40.0 F capacitor. What is the voltage across the capacitor?(A) 2.8 V (B) 4.0 V (C) 2.8 kV (D) 4.0 kV (E) 2.8 MV

9. The figure shows three electric charges labeled Q1, Q2, Q3, and someelectric field lines in the region surrounding the charges. What are thesigns of the three charges?(A) Q1 is negative, Q2 is positive, Q3 is negative.(B) Q1 is positive, Q2 is positive, Q3 is negative.(C) Q1 is positive, Q2 is negative, Q3 is positive.(D) Q1 is positive, Q2 is negative, Q3 is negative.(E) Q1 is negative, Q2 is negative, Q3 is negative.

11. A DC voltage of 110 V is applied to a heater whose resistance is 15 Ohms when it is hot. At whatrate is electrical energy transferred to thermal energy _____.(A) 807 W (B) 1650 W (C) 8150 W (D) 12375 W (E) 24750 W

12. A wave has an angular frequency of 110 rad/s and a wavelength of 1.8 m. Calculate the angularwave number.(A) (B) (C) (D) (E)

13. A transverse wave traveling along a string transports energy at a rate r. If we want to double thisrate, we could increase the amplitude of the wave by a factor of _____.(A) 8 (B) 4 (C) 2 (D) √2 (E) √8

14. A 2.0 m string is fixed at both ends and tightened until the wave speed is 80 m/s. What is the frequency of the standing wave shown in the figure?(A) 60 Hz (B) 120 Hz (C) 240 Hz (D) 360 Hz (E) 480 Hz

15. The speed of yellow light (from a sodium lamp) in a certain liquid is measured to be 1.92 × 108m/s. What is the index of refraction of this liquid for the light?(A) 1.49 (B) 1.53 (C) 1.56 (D) 1.62 (E) 1.67

16. Which of the following statements is incorrect?(A) The emission spectrum of hydrogen contains a discontinuum of colors.(B) Diffraction produces both constructive and destructive interference.(C) All matter exhibits both particle and wavelike characteristics.(D) Niels Bohr developed a quantum model for the hydrogen atom.(E) None of the above.