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  • An object is released from rest a height h above the ground. A second object with four times the mass of the first if released from the same height. The potential energy of the second object compared to the first is Question 11 Answer a. one-fourth as much. b. four times as much. c. twice as much. d. one-half as much.

An object is released from rest a height h above the ground. A second object with four times the mass of the first if released from the same height. The potential energy of the second object compared to the first is Question 11 Answer a. one-fourth as much. b. four times as much. c. twice as much. d. one-half as much.

Answer

  • Answer

Answer: b. four times as much.

Explanation: The potential energy (PE) of an object at a height \( h \) is given by the formula:

\[ \text{PE} = mgh \]

where \( m \) is the mass of the object, \( g \) is the acceleration due to gravity, and \( h \) is the height above the ground.

If the second object has four times the mass of the first object, then its potential energy will be:

\[ \text{PE}_{\text{second}} = 4m \cdot g \cdot h = 4(mgh) \]

This means the potential energy of the second object is four times that of the first object.

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(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H + HO2 → O2 + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O2 k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) H + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-5 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M⁻¹ s⁻¹) 1 OH + H₂ → H + H₂O 3.74 x 10⁷ 2 OH + HO₂ → HO₂ + OH⁻ 5 x 10⁹ 3 OH + H₂O₂ → HO₂ + H₂O 3.8 x 10⁷ 4 OH + O₂ → O₂ + OH 9.96 x 10⁹ 5 OH + HO₂ → O₂ + H₂O 7.1 x 10⁹ 6 OH + OH → H₂O₂ 5.3 x 10⁹ 7 OH + e⁻aq → OH⁻ 3 x 10¹⁰ 8 H + O₂ → HO₂ 2.0 x 10¹⁰ 9 H + HO₂ → H₂O₂ 2.0 x 10¹⁰ 10 H + H₂O₂ → OH + H₂O 3.44 x 10⁷ 11 H + OH → H₂O 1.4 x 10¹⁰ 12 H + H → H₂ 1.94 x 10¹⁰ 13 e⁻aq + O₂ → O₂⁻ 1.9 x 10¹⁰ 14 e⁻aq + O₂ → HO₂⁻ + OH⁻ 1.3 x 10¹⁰ 15 e⁻aq + HO₂ 2.0 x 10¹⁰ 16 e⁻aq + H₂O₂ 1.1 x 10¹⁰ 17 e⁻aq + HO₂ → OH + OH⁻ 1.3 x 10¹⁰ 18 e⁻aq + H⁺ → H 2.3 x 10¹⁰ 19 e⁻aq + e⁻aq → H₂ + OH⁻ + OH⁻ 2.5 x 10⁹ 20 HO₂ + O₂ → O₂ + HO₂ 1.3 x 10⁹ 21 HO₂ + HO₂ → O₂ + H₂O₂ 8.3 x 10⁵ 22 HO₂ + HO₂ → O₂ + OH + H₂O 3.7 23 HO₂ + HO₂ → O₂ + O₂ + OH + H₂O 7 x 10⁵ s⁻¹ 24 H⁺ + O₂⁻ → HO₂ 4.5 x 10¹⁰ 25 H⁺ + O₂⁻ → O₂ 2.0 x 10¹⁰ 26 H⁺ + OH⁻ 1.4 x 10¹¹ 27 H⁺ + HO₂⁻ 2 x 10¹⁰ 28 H₂O₂ → HO₂ + H⁺ + OH⁻ 2.5 x 10⁻⁵ s⁻¹ 29 H₂O₂ → H⁺ + OH⁻ 1.4 x 10⁻⁷ s⁻¹ 30 O₂ + O₂ → O₂ + HO₂ + OH⁻ 0.3 31 O₂ + H₂O₂ → O₂ + OH + OH 16 32

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O + O → 2 OH k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ

Table 1 Reactions, rate constants and activation energies used in the model* No. Reaction kopt (M−1 s−1) 1 OH + H2 → H + H2O 3.74 x 107 2 OH + HO2 → HO2 + OH− 5 x 109 3 OH + H2O2 → HO2 + H2O 3.8 x 107 4 OH + O2 → O2− + OH 9.96 x 109 5 OH + HO2 → O2 + H2O 7.1 x 109 6 OH + OH → H2O2 5.3 x 109 7 OH + eaq− → OH− 3 x 1010 8 OH + O2− → HO2 2.0 x 1010 9 H + O2 → HO2 2.0 x 1010 10 H + HO2 → H2O2 2.0 x 1010 11 H + H2O2 → OH + H2O 3.4 x 107 12 H + OH → H2O 1.4 x 1010 13 H + H → H2 7.9 x 109 14 eaq− + O2 → O2− 1.94 x 1010 15 eaq− + O2− → HO2− + OH− 1.3 x 1010 16 eaq− + HO2 → OH− + OH 2.5 x 1010 17 eaq− + H2O2 → OH + OH− 1.3 x 1010 18 eaq− + H → H− 2.5 x 1010 19 eaq− + eaq− + H2 + OH− 3.5 x 109 20 eaq− + H2O2 + OH− 4.5 x 109 21 HO2 + O2 → O2 + HO2 3.7 22 HO2 + HO2 → O2 + H2O2 3.7 23 HO2 + HO2 → O2 + OH + H2O 7 x 105 s−1 24 HO2− + O2 4.5 x 1010 25 H2O2 → 2OH 0.035 s−1 26 H+ + O2− → HO2 2 x 1010 27 H+ + HO2− → HO2 2 x 1010 28 H2O2 → H+ + HO2− 2.5 x 10−5 s−1 29 H2O2 → H+ + HO2− 2.5 x 10−5 s−1 30 O2− + O2 → HO2 + OH− 0.3 31 O2− + H2O2 → O2 + OH− + OH 16 32 1.8 x 107

(2) O3 + H → O2 + OH k2 = 1.78×10^-11 cm^3 s^-1 (3) O + OH → O2 + H k3 = 4.40×10^-11 cm^3 s^-1 (5) O + HO2 → O2 + OH k5 = 3.50×10^-11 cm^3 s^-1 (6) H2O → O + H2 k6 = 5.40×10^-12 cm^3 s^-1 (9) OH + HO2 → O2 + H2O k9 = 4.00×10^-11 cm^3 s^-1 (10) HO2 + HO2 → O2 + H2O2 k10 = 2.50×10^-12 cm s^-1 (11) O + O2 + M → O3 + M k11 = 1.05×10^-34 cm^6 s^-1 (14) H + O2 + M → HO2 + M k14 = 8.08×10^-32 cm^6 s^-1 (15) OH + H + M → H2O + M k15 = 3.31×10^-27 cm^6 s^-1 (16) O2 + hv → 2 O k16 = (1.26×10^-8 s^-1) φ (17) H2O + hv → H + OH k17 = (3.4×10^-6 s^-1) φ (18) O3 + hv → O2 + O k18 = (7.10×10^-8 s^-1) φ