Concept explainers
(a)
Interpretation:
The equation of motion that describes the given system is to be stated.
Concept introduction:
Newton’s law of motion gives the relation between the forces acting on a system and the motion of the system.
The Lagrangian function is the formulation of the
(b)
Interpretation:
The equation of motion describing the given system is to be stated.
Concept introduction:
Newton’s law of motion gives the relation between the forces acting on a system and the motion of the system.
The Lagrangian function is the formulation of the classical mechanics. According to mechanics, the Lagrangian function is the difference of kinetic energy and potential energy which is expressed as functions of positions and velocity.
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Physical Chemistry
- Two nitro (NO2) groups are chemically bonded to a patch of surface. They can't move to another location on the surface, but they can rotate (see sketch at right). It turns out that the amount of rotational kinetic energy each NO2 group can have is required to be a multiple of €, where € = 1.0 × 1024 J. In other words, each NO2 group could have & of rotational kinetic energy, or 2ɛ, or 3%, and so forth - but it cannot have just any old amount of rotational kinetic energy. Suppose the total rotational kinetic energy in this system is initially known to be 87. Then, some heat is removed from the system, and the total rotational kinetic energy falls to 59. Calculate the change in entropy. Round your answer to 3 significant digits, and be sure it has the correct unit symbol. Two rotating NO2 groups bonded to a surface. x10 ☐ ☐ 1 Garrow_forwardwhere m stands for the mass of the particle, v stands for the particle speed, T stands for the Temperature of the system, and k stands for the Boltzmann constant. What would be the relative average kinetic energies for the helium, neon, and argon at 100K? (think about what this would mean for each variable) Explain how you assigned the relative positions of each gas.arrow_forwardA N2 molecule at 20 ⁰C is released at sea level to travel upward. Assuming that the molecule does not collide with other molecules, how far will it travel before coming to rest? Do the same calculation for a He atom. Hint: to calculate the height h, the molecule will travel, equate its kinetic energy with the potential energy it attains at h, which is mgh. Here m is the mass, and g is the gravitational accelerationarrow_forward
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- I would like an explanation on how to work this problem out, because I got it incorrect.arrow_forwardAt a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its speed is being increased at the rate of 8 m/s2. Airplane B is flying at the same altitude as airplane A and, as it rounds a pylon, is following a circular path of 300-m radius. Knowing that at the given instant the speed of B is being decreased at the rate of 3 m/s2, determine, for the positions shown, (a) the velocity of B relative to A, (b) the acceleration of B relative to A.arrow_forwardIf a liter of argon gas (Ar) is compared to a liter of neon gas (Ne), both at 75°C and two atmospheres of pressure, then: The Ne atoms are on the average moving more slowly than the Ar atoms. The average kinetic energy of the Ar atoms is greater than that of the Ne atoms. O The mass of one liter of Ar equals the mass of one liter of Ne. There are equal numbers of Ar and Ne atoms. The Ar and Ne atoms have the same average speed.arrow_forward
- The bonds that hold the atoms in a molecule together behave like simple springs. As a result, atmospheric molecules oscillate at frequencies similar to that of infrared radiation, so that these molecules can both absorb and emit infrared radiation (i.e., resonance). Make a simple sketch to illustrate the greenhouse effect by showing:- infrared radiation originating at the Earth’s surface- a carbon dioxide molecule (with springs) in the atmosphere- any radiation absorbed by the molecules being reemitted in a random directionWhy does the presence of the molecule change the Earth’s temperature?arrow_forward3. Answer the following questions at 75 °C and 1 mole assuming all possible energy states are populated (i) (ii) (iii) (iv) (v) (vi) (vii) the root mean square speed of O2 molecules (viii) translational energies of He atoms (іх) (х) the mean speeds of He atoms the mean speeds of Hg atoms ratio of the mean speeds of He and Hg atoms most probable speed of He atoms ratio of the most probable speeds of He and Hg atoms the mean relative speed of H2 molecules vibrational energies of He atoms rotational energies of He atomsarrow_forward2.Oxygen travels at a velocity of 29.0 m/s. At what velocity would SF4 travel under the same conditions?arrow_forward
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