27.The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U (x)=-a/x¹² -b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ¥)?(b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance? Solution a. -2a b 1/6 ; b. 0; c. ~x6

27.The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U (x)=-a/x¹² -b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ¥)?(b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance? Solution a. -2a b 1/6 ; b. 0; c. ~x6

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

See similar textbooks

Related questions

Q: A 49-kg box is being pushed a distance of 7.2 m across the floor by a force P whose magnitude is 189…

Q: Calculate A) the conservative force described by the potential energy function U(x,y,z) = ½ k (2x³…

A: A) In case of conservative force, we know that force is the negative gradient of potential energy.…

Q: A 7.80-g bullet moving at 690 m/s penetrates a tree trunk to a depth of 6.20 cm. (a) Use work and…

A: Mass of bullet (mb)=7.8 g Initial speed of the bullet (u)=690 m/s Penetration in trunk (d)=6.2 cm

Q: -kx³. The work required to stretch the 0 to the stretched length x = l is Wo. In terms of A "stiff"…

Q: 1. Drops frequently form above the ocean by the mechanical disruption of waves in strong winds. How…

Q: The potential energy due to two particles separated by distance ris -- where a and B are constants.…

A: thank you

Q: An assistant for a football team carries a 32.0 kg cooler of water from the top row of the stadium,…

A: The expression to solve for the work done by the assistant is as follows: WA=KEf-KEi+PEf-PEi…

Q: In the figure, a 2.12 g ice flake is released from the edge of a hemispherical bowl whose radius r…

A: mass of ice flake = 2.12 gradius (r) = 16.2 cm = 0.162 m surface type = frictionless

Q: 1. Find the force for each of the following potential energy functions: (a) V = cxyz + C (b) V = ax²…

A: The objective of the question is to find the force for given potential energy functions, determine…

Q: For a system of two particles we often let the potential energy for the force between the particles…

A: The potential energy is positive for repelling particles, and it has its maximum value if they are…

Q: Problem #2: a. How high a hill can a car coast up (engines disengaged) if work done by friction is…

Q: For energy transfer through a material do I use... P=kA(Th-Tc)/L or P=ka*((Th-Tc)/L) Some…

Q: The equation that describes the potential energy stored in the interaction between two atoms in a…

Q: Q6) A block of mass m = 1.18 kg is moving on a horizontal surface subject to a force with UO al²+y²)…

Q: A 7.80-g bullet moving at 575 m/s penetrates a tree trunk to a depth of 5.50 cm. (a) Use work and…

A: a) as the bullet is penetrating into the tree truck, the only force excites here is, the average…

Q: A 0.4 Gram mass is required to stretch a soap film confined in arectangular frame by 2mm downward…

A: Mass of the object m=0.4 g so force applied by the weight of the object F=mg=0.4*9.8*10-3=3.92*10-3N…

Q: A 41.0 kg box initially at rest is pushed 5.55 m along a rough, horizontal floor with a constant…

Q: Consider a particle moving under the influence of the potential a U(x) = U, a where U>0 and a>0.…

A: Given, the potential is Ux=Uoax+xa where Uo>0 and a>0 And its graph is For the equilibrium…

Q: Don't use Artificial intelligence tools. Only Handwritten solutions are allowed. Mechanical…

A: This total energy per unit weight includes all the potential energy, kinetic energy, and pressure…

Q: You place a wooden 1 meter ruler flat on a table. You place a penny flat on the ruler and exactly…

A: Given quantities: Mass of the penny (m) = 2.5 grams coefficient of friction between wood and metal…

Q: b- Given the two- dimensional potential energy function V (r) = Vo 1 k 82 e-r2182 Where r = xi + yj…

A: Given: V(r) = Vo - (1/2) kδ2 e-r2/δ2

Q: In the figure, a 2.30 g ice flake is released from the edge of a hemispherical bowl whose radius r…

A: Since you have asked multi-part questions, we will solve the first three parts for you. In case…

Q: The average power output of the human heart is 1.33 watts.(a) How much energy does the heart produce…

A: Power is Time is Note:Find:(a) Energy produces by human heart in one day.(b) Estimate the height a…

Q: The propellers of a drone require a force of 70 N to lift, at constant speed, a parcel from the…

A: thank you

Q: The potential energy of two atoms in a diatomic molecule can be approximated by the Lennard- Jones…

Q: The force on a particle is described by the function: F(y) = -b+ay+ where a and b are constants and…

A: Force , F(y) = -b + a y4 Potential U(y) is given as U(y)=−∂F∂y=−4ay3U(y)=-∂F∂y=-4ay3

Concept explainers

Maxwell speed distribution

Maxwell-Boltzmann distribution or commonly known as Maxwell speed distribution, explains the division of the energy levels of the molecules of an ideal gas on the basis of the statistical theory. In 1859, Scottish physicist James Clerk Maxwell established the context for the distribution of molecular velocities for random molecules moving in a closed environment. This theory was generalized in 1871 by German physicist Ludwig Boltzmann. He improvised the theory to express the distribution of energy levels among different molecules.

Question

27.The potential energy function for either one of the two atoms in a diatomic molecule is often
approximated by U (x)=-a/x¹² -b/x6 where x is the distance between the atoms. (a) At what
distance of seperation does the potential energy have a local minimum (not at x = ¥)?(b) What
is the force on an atom at this separation? (c) How does the force vary with the separation
distance?
Solution
a.
-2a
b
1/6
; b. 0; c. ~x6

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

19 4
1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U(r) = ax' – bx ax³ a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.
1. A 0.20-kg stone is held 1.3 m above the top edge of a water well and then dropped into it. The well has a depth of 5.0 m. Relative to the configuration with the stone at the top edge of the well, what is the gravitational potential energy of the stone-Earth system (a) before the stone is released and (b) when it reaches the bottom of the well? (c) What is the change in gravitational potential energy of the system from release to reaching the bottom of the well?
1. When is work done on an object? O When a force is applied to an object and the object moves in the same direction as the force When a force is applied on an object and the object remains stationary When the frictional force on an object is greater than a force applied to an object When two forces of equal magnitude are applied to the object in opposite directions
2 A block of mass m is lowered down a surface inclined at θ degrees for a distance d between points A and B. A horizontal force F is acting on the block between A and B. Take the kinetic energy of the block at points A and B as KA and KB, respectively. (a) Construct an analytic expression to determine how much work is done on the block by the force of friction between points A and B. (b) Now determine the actual amount of work done in (a) above, if the block has a mass of 4.0 kg, the angle of inclination, is θ = 37, the distance d = 5.0 m, KA = 10 J and KB = 20 J.
1. A particle moves in one dimension and is subject to a conservative force, whose potential energy function is given by U(x), where a and b are positive constants. U ( x ) = a x 3 − b x a) Find the two equilibrium positions of the particle. b) For each of the two equilibrium positions, determine whether the equilibrium is stable or unstable.
1. Some species of whales can dive to depths of 800m. What is the total pressure they experience at this depth? (The density of sea water = 1020 kg/m, and 1 ATM =10$ N/m) A 15.0-kg object is pulled along a horizontal surface at a constant speed by a 25 N force acting at 30° above the horizontal. How much work is done by this force as the object moves 10.0 m? A force of F = 3i + 0.5j – 5k), N is applied to a particle located at r = 2i +4k, m. Determine a) The torque vector; b) The angle between the vectors F and r 3. 4. A ball of mass Mi = 0.250 kg and velocity Voi = +5.00 m/s collides head-on with a ball of mass M2 = 0.800 kg initially at rest. No external forces act on the balls. If the collision is perfectly inelastic, find the velocity of mi after collision? Voi M1 M2 2.
A force of 30 N acts on an object with mass 5kg, and the object is displaced 10 m along a rough surface. The coefficient of kinetic friction between the object and the surface is 0.35. Calculate the work done by friction.
3. Suppose you have an object attached to a bizarre spring, initially located at x = 0, the equilibrium point of the force of the spring on the object is given by F₁ = kx, S where k is a spring constant. (a) You displace the object from x = 0 to ₁ > 0, holding the object steady at the beginning and end. What is the work done by the spring? What is the work done by you? (b) You let go of the spring and observe the object move from location. x₁ to x2. Is x2 less than or greater than ₁? (c) What is the kinetic energy of the object at x2? (d) Is this bizarre spring realistic? Explain.
A force F→ is applied to a 2.0 kg, radio-controlled model car parallel to the x-axis as it moves along a straight track. Calculate the work done by the force F→ when the car moves from x = 0 to x = 3.0 m. Calculate the work done by the force F→ when the car moves from x = 4.0 m to x = 7.0 m.
In the figure, a 3.97 g ice flake is released from the edge of a hemispherical bowl whose radius ris 13.7 cm. The flake-bowl contact is frictionless. (a) How much work is done on the flake by the gravitational force during the flake's descent to the bottom of the bowl? (b) What is the change in the potential energy of the flake-Earth system during that descent? (c) If that potential energy is taken to be zero at the bottom of the bowl, what is its value when the flake is released? (d) If, instead, the potential energy is taken to be zero at the release point, what is its value when the flake reaches the bottom of the bowl? (a) Number (b) Number -5.34e-3 (c) Number 5.34e-3 (d) Number 5.34e-3 Units Units Units Ice flake- Mik Units J
The potential energy function for either one of the two atoms in a diatomic molecule is often approximated by U(x) = −a/x12 − b/x6 where x is the distance between the atoms. (a) At what distance of seperation does the potential energy have a local minimum (not at x = ∞)? (b) What is the force on an atom at this separation? (c) How does the force vary with the separation distance?