University Physics with Modern Physics (14th Edition)
14th Edition
ISBN: 9780321973610
Author: Hugh D. Young, Roger A. Freedman
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 7, Problem 7.35E
CALC The potential energy of two atoms in a diatomic molecule is approximated by U(r) = (a/r12) − (b/r6), where r is the spacing between atoms and a and b are positive constants, (a) Find the force F(r) on one atom as a function of r. Draw two graphs: one of U(r) versus r and one of F(r) versus r. (b) Find the equilibrium distance between the two atoms. Is this equilibrium stable? (c) Suppose the distance between the two atoms is equal to the equilibrium distance found in part (b). What minimum energy must be added to the molecule to dissociate it—that is, to separate the two atoms to an infinite distance apart? This is called the dissociation energy of the molecule, (d) For the molecule CO, the equilibrium distance between the carbon and oxygen atoms is 1.13 × 10 −10 m and the dissociation energy is 1.54 × 10−18 J per molecule. Find the values of the constants a and b.
Expert Solution & Answer
Learn your wayIncludes step-by-step video
schedule13:52
Students have asked these similar questions
One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is
U(r)=U0[(r0/r)12−(r0/r)4]
where r0 = 0.65 nm and U0 = 7.4 eV.Note: 1 eV = 1.6×10−19 J.Some helpful units:[Force] = eV/nm[Energy] = eV[distance] = nm
Here is what I am having trouble with:
You can choose where the potential energy equals zero anywhere you want (you can add or subtract any constant to it). For this function, U(∞) = 0. This is very common for electromagnetic problems like you will see in Physics 2. If the potential energy function were defined as
U(r)=U0[(r0/r)12−(r0/r)4]+U1
where U1 = 4.5 eV, reanswer all of the previous questions using this new potential energy function.
req= ?
Fr(req+r1)= ?
K(req)= ?
(NOTE: these are all part of the same question)
I got .957026 nm for req, and -1.4348 eV/nm for Fr(req+r1), and I couldnt get an answer for K(req). My answers are wrong. Where am I not understanding?
In physics, the work done on an object is equal to the integral of the force on that object dotted with its displacent.
This looks like W = |(F-ds) (W is work, F is force, and ds is the infinitesimally small displacement vector). For a force whose direction
is the line of motion, the equation becomes W = /(Fdz).
If the force on an object as a function of displacement is F(z) = 3z² + z, what is the work as a function of displacement W(z)?Assume
W(0) = 0 and the force is in the direction of the object's motion.
One model for the potential energy of a two-atom molecule, where the atoms are separated by a distance r, is
U(r)=U0[(r0/r)12−(r0/r)4]
where r0 = 0.65 nm and U0 = 7.4 eV.Note: 1 eV = 1.6×10−19 J.Some helpful units:[Force] = eV/nm[Energy] = eV[distance] = nm
Here is what I am having trouble with:
What is the distance between the atoms when the molecule is in stable equilibrium?
If the distance between the atoms increases from equilibrium by r1 = 0.2 nm, then what is the force from one atom on the other associated with this potential energy? (Enter your answer as postive if they repel each other, and negative if they attract.)
Chapter 7 Solutions
University Physics with Modern Physics (14th Edition)
Ch. 7.1 - The figure shows two friction-less ramps. The...Ch. 7.2 - Consider the situation in Example 7.9 at the...Ch. 7.3 - In a hydroelectric generating station, falling...Ch. 7.4 - A particle moving along the x-axis is acted on by...Ch. 7.5 - The curve in Fig. 7.24b has a maximum at a point...Ch. 7 - A baseball is thrown straight up with initial...Ch. 7 - A projectile has the same initial kinetic energy...Ch. 7 - An object is released from rest at the top of a...Ch. 7 - An egg is released from rest from the roof of a...Ch. 7 - A physics teacher had a howling hall suspended...
Ch. 7 - Is it possible for a friction force to increase...Ch. 7 - A woman bounces on a trampoline, going a little...Ch. 7 - Fractured Physics. People often call their...Ch. 7 - (a) A book is lifted upward a vertical distance of...Ch. 7 - (a) A block of wood is pushed against a spring,...Ch. 7 - A 1.0-kg stone and a 10.0-kg stone are released...Ch. 7 - Two objects with different masses are launched...Ch. 7 - When people are cold, they often rub their hands...Ch. 7 - A box slides down a ramp and work is done on the...Ch. 7 - In physical terms, explain why friction is a...Ch. 7 - Since only changes in potential energy are...Ch. 7 - Figure 7.22a shows the potential-energy function...Ch. 7 - Figure 7.22b shows the potential-energy function...Ch. 7 - For a system of two particles we often let the...Ch. 7 - Explain why the points x = A and x = A in Fig....Ch. 7 - A particle is in neutral equilibrium if the net...Ch. 7 - The net force on a particle of mass m has the...Ch. 7 - The potential-energy function for a force F is...Ch. 7 - In one day, a 75-kg mountain climber ascends from...Ch. 7 - BIO How High Can We Jump? The maximum height a...Ch. 7 - CP A 90.0-kg mail bag hangs by a vertical rope 3.5...Ch. 7 - BIO Food Calories. The food calorie, equal to 4186...Ch. 7 - A baseball is thrown from the roof of a...Ch. 7 - A crate of mass M starts from rest at the top of a...Ch. 7 - BIO Human Energy vs. Insect Energy. For its size,...Ch. 7 - Prob. 7.8ECh. 7 - Prob. 7.9ECh. 7 - A 25.0-kg child plays on a swing having support...Ch. 7 - You are testing a new amusement park roller...Ch. 7 - Tarzan and Jane. Tarzan, in one tree, sights Jane...Ch. 7 - CP A 10.0-kg microwave oven is pushed 6.00 m up...Ch. 7 - An ideal spring of negligible mass is 12.00 cm...Ch. 7 - A force of 520 N keeps a certain spring stretched...Ch. 7 - BIO Tendons. Tendons are strong elastic fibers...Ch. 7 - A spring stores potential energy U0 when it is...Ch. 7 - A slingshot will shoot a 10-g pebble 22.0 m...Ch. 7 - A spring of negligible mass has force constant k =...Ch. 7 - A 1.20-kg piece of cheese is placed on a vertical...Ch. 7 - A spring of negligible mass has force constant k =...Ch. 7 - (a) For the elevator of Example 7.9 (Section 7.2),...Ch. 7 - A 2.50-kg mass is pushed against a horizontal...Ch. 7 - A 2.50-kg block on a horizontal floor is attached...Ch. 7 - You are asked to design a spring that will give a...Ch. 7 - A 75-kg roofer climbs a vertical 7.0-m ladder to...Ch. 7 - A 0.60-kg book slides on a horizontal table. The...Ch. 7 - CALC In an experiment, one of the forces exerted...Ch. 7 - A 62.0-kg skier is moving at 6.50 m/s on a...Ch. 7 - Vector A is in the direction 34.0 clockwise from...Ch. 7 - CALC A force parallel to the .v-axis acts on a...Ch. 7 - CALC The potential energy of a pair of hydrogen...Ch. 7 - CALC A small block with mass 0.0400 kg is moving...Ch. 7 - CALC An object moving in the xy-plane is acted on...Ch. 7 - CALC The potential energy of two atoms in a...Ch. 7 - A marble moves along the x-axis. The...Ch. 7 - At a construction site, a 65.0-kg bucket of...Ch. 7 - Two blocks with different masses are attached to...Ch. 7 - A block with mass 0.50 kg is forced against a...Ch. 7 - A 2.00-kg block is pushed against a spring with...Ch. 7 - A 2.00-kg block is pushed against a spring with...Ch. 7 - CP Riding a Loop-the- Loop. A car in an amusement...Ch. 7 - A 2.0-kg piece of wood slides on a curved surface...Ch. 7 - Up and Down the Hill. A 28-kg rock approaches the...Ch. 7 - A 15.0-kg stone slides down a snow-covered hill...Ch. 7 - CP A 2.8-kg block slides over the smooth, icy hill...Ch. 7 - Bungee Jump. A bungee cord is 30.0 m long and,...Ch. 7 - You are designing a delivery ramp for crates...Ch. 7 - The Great Sandini is a 60-kg circus performer who...Ch. 7 - A 1500-kg rocket is to be launched with an initial...Ch. 7 - A system of two paint buckets connected by a...Ch. 7 - These results are from a computer simulation for a...Ch. 7 - CP A 0.300-kg potato is tied to a string with...Ch. 7 - A 60.0-kg skier starts from rest at the top of a...Ch. 7 - Prob. 7.55PCh. 7 - A ball is thrown upward with an initial velocity...Ch. 7 - Prob. 7.57PCh. 7 - A truck with mass m has a brake failure while...Ch. 7 - CALC A certain spring found not to obey Hookes law...Ch. 7 - CP A sled with rider having a combined mass of 125...Ch. 7 - CALC A conservative force F is in the +x-direction...Ch. 7 - A 3.00-kg block is connected to two ideal...Ch. 7 - A 0.150-kg block of ice is placed against a...Ch. 7 - If a fish is attached to a vertical spring and...Ch. 7 - CALC You are an industrial engineer with a...Ch. 7 - A basket of negligible weight hangs from a...Ch. 7 - CALC A 3.00-kg fish is attached to the lower end...Ch. 7 - You are designing an amusement park ride. A cart...Ch. 7 - A 0.500-kg block, attached to a spring with length...Ch. 7 - CP A small block with mass 0.0400 kg slides in a...Ch. 7 - CP A small block with mass 0.0500 kg slides in a...Ch. 7 - CP Pendulum. A small rock with mass 0.12 kg is...Ch. 7 - A wooden block with mass 1.50 kg is placed against...Ch. 7 - CALC A small object with mass m = 0.0900 kg moves...Ch. 7 - CALC A cutting tool under microprocessor control...Ch. 7 - A particle moves along the x-axis while acted on...Ch. 7 - Prob. 7.77PCh. 7 - DATA A long ramp made of cast iron is sloped at a...Ch. 7 - DATA A single conservative force F(x) acts on a...Ch. 7 - CALC A proton with mass m moves in one dimension....Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...Ch. 7 - BIO THE DNA SPRING. A DNA molecule, with its...
Additional Science Textbook Solutions
Find more solutions based on key concepts
What is the difference between cellular respiration and external respiration?
Human Physiology: An Integrated Approach (8th Edition)
Identify each of the following reproductive barriers as prezygotic or postzygotic. a. One lilac species lives o...
Campbell Essential Biology with Physiology (5th Edition)
All of the following terms can appropriately describe humans except: a. primary consumer b. autotroph c. hetero...
Human Biology: Concepts and Current Issues (8th Edition)
Modified True/False 6. __________ Halophiles inhabit extremely saline habitats, such as the Great Salt Lake.
Microbiology with Diseases by Body System (5th Edition)
Describe an example of bioconversion. What metabolic processes can result in fuels?
Microbiology: An Introduction
Use a globe or map to determine, as accurately as possible, the latitude and longitude of Athens, Greece.
Applications and Investigations in Earth Science (9th Edition)
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
- (a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.arrow_forwardA particle moves in the xy plane (Fig. P9.30) from the origin to a point having coordinates x = 7.00 m and y = 4.00 m under the influence of a force given by F=3y2+x. a. What is the work done on the particle by the force F if it moves along path 1 (shown in red)? b. What is the work done on the particle by the force F if it moves along path 2 (shown in blue)? c. What is the work done on the particle by the force F if it moves along path 3 (shown in green)? d. Is the force F conservative or nonconservative? Explain. FIGURE P9.30 In each case, the work is found using the integral of Fdr along the path (Equation 9.21). W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz) (a) The work done along path 1, we first need to integrate along dr=dxi from (0,0) to (7,0) and then along dr=dyj from (7,0) to (7,4): W1=x=0;y=0x=7;y=0(3y2i+xj)(dxi)+x=7;y=0x=7;y=4(3y2i+xj)(dyj) Performing the dot products, we get W1=x=0;y=0x=7;y=03y2dx+x=7;y=0x=7;y=4xdy Along the first part of this path, y = 0 therefore the first integral equals zero. For the second integral, x is constant and can be pulled out of the integral, and we can evaluate dy. W1=0+x=7;y=0x=7;y=4xdy=xy|x=7;y=0x=7;y=4=28J (b) The work done along path 2 is along dr=dyj from (0,0) to (0,4) and then along dr=dxi from (0,4) to (7,4): W2=x=0;y=0x=0;y=4(3y2i+xj)(dyj)+x=0;y=4x=7;y=4(3y2i+xj)(dyi) Performing the dot product, we get: W2=x=0;y=0x=0;y=4xdy+x=0;y=4x=7;y=43y2dx Along the first part of this path, x = 0. Therefore, the first integral equals zero. For the second integral, y is constant and can be pulled out of the integral, and we can evaluate dx. W2=0+3y2x|x=0;y=4x=7;y=4=336J (c) To find the work along the third path, we first write the expression for the work integral. W=rtrfFdr=rtrf(Fxdx+Fydy+Fzdz)W=rtrf(3y2dx+xdy)(1) At first glance, this appears quite simple, but we cant integrate xdy=xy like we might have above because the value of x changes as we vary y (i.e., x is a function of y.) [In parts (a) and (b), on a straight horizontal or vertical line, only x or y changes]. One approach is to parameterize both x and y as a function of another variable, say t, and write each integral in terms of only x or y. Constraining dr to be along the desired line, we can relate dx and dy: tan=dydxdy=tandxanddx=dytan(2) Now, use equation (2) in (1) to express each integral in terms of only one variable. W=x=0;y=0x=7;y=43y2dx+x=0;y=0x=7;y=4xdyW=y=0y=43y2dytan+x=0x=7xtandx We can determine the tangent of the angle, which is constant (the angle is the angle of the line with respect to the horizontal). tan=4.007.00=0.570 Insert the value of the tangent and solve the integrals. W=30.570y33|y=0y=4+0.570x22|x=0x=7W=112+14=126J (d) Since the work done is not path-independent, this is non-conservative force. Figure P9.30ANSarrow_forward(a) For what values of the angle between two vectors is their scalar product positive? (b) For what values of is their scalar product negative?arrow_forward
- If the net work done by external forces on a particle is zero, which of the following statements about the particle must be true? (a) Its velocity is zero. (b) Its velocity is decreased. (c) Its velocity is unchanged. (d) Its speed is unchanged. (e) More information is needed.arrow_forwardA shopper weighs 3.00 kg of apples on a supermarket scale whose spring obeys Hookes law and notes that the spring stretches a distance of 3.00 cm. a. What will the springs extension be if 5.00 kg of oranges are weighed instead? b. What is the total amount of work that the shopper must do to stretch this spring a total distance of 7.00 cm beyond its relaxed position?arrow_forwardA constant force of magnitude 4.75 N is exerted on an object. The forces direction is 60.0 counterclockwise from the positive x axis in the xy plane, and the objects displacement is r=(4.22.1j+1.6k)m. Calculate the work done by this force.arrow_forward
- Recall that the work WW done by a constant force F⃗ F→ at an angle θθ to the displacement Δr⃗ Δr→ is W=F⃗ ⋅Δr⃗ =FΔrcosθW=F→⋅Δr→=FΔrcosθ. The vector magnitudes FF and ΔrΔr are always positive, so the sign of WW is determined entirely by the angle θθ between the force and the displacement. What is the work WnWn done on the box by the normal force? Express your answers in joules to two significant figures What is the work WTWT done by the tension force? Express your answers in joules to two significant figures.arrow_forwardNeeds Complete typed solution with 100 % accuracy.arrow_forwardFind the work done by the vector field F = (– 3z, 4y, – x) in moving an object along C in the positive direction, where C is given by r(t) = (t, sin(t), cos(t)), 0 < tarrow_forward3) The equation that describes the potential energy stored in the interaction between two atoms in a diatomic molecule is U = A/x12 – B/x6. Here A and B are appropriate constants and x is the inter-atomic distance. Find the magnitude of the force that one atom exerts on the other. a) 12A/x13 – 6B/x7 b) –13A/x13 + 7B/x7 c) –11A/x11 + 5B/x5 d) 72A/x12 – 72B/x6 e) A/x13 – B/x7arrow_forwardRecall that the work WWW done by a constant force F⃗ F→F_vec at an angle θθtheta to the displacement Δr⃗ Δr→ is W=F⃗ ⋅Δr⃗ =FΔrcosθW=F→⋅Δr→=FΔrcosθ. The vector magnitudes FFF and ΔrΔr are always positive, so the sign of WWW is determined entirely by the angle θθtheta between the force and the displacement. What is the work WTWT done by the tension force? Express your answers in joules to two significant figures.arrow_forwardQ1/ The work done on an object is equal to the integral of the force on that object dotted with its displacent. This looks like W=[(F.ds) (W is work, F is force, and ds is the infinitesimally small displacement vector). For a force whose direction is the line of motion, the equation becomes W=[(Fdx). If the force on an object as a function of displacement is F(x)=3x2+x, what is the work as a function of displacement (using calculus application) W(x)? Assume W(0)=0 and the force is in the direction of the object's motion.arrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
Recommended textbooks for you
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...PhysicsISBN:9781337553292Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and EngineersPhysicsISBN:9781337553278Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
College PhysicsPhysicsISBN:9781305952300Author:Raymond A. Serway, Chris VuillePublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Physics for Scientists and Engineers
Physics
ISBN:9781337553278
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
Publisher:Cengage Learning
College Physics
Physics
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Cengage Learning
Kinetic Energy and Potential Energy; Author: Professor Dave explains;https://www.youtube.com/watch?v=g7u6pIfUVy4;License: Standard YouTube License, CC-BY