EBK ESSENTIAL UNIVERSITY PHYSICS, VOLUM
4th Edition
ISBN: 9780135272947
Author: Wolfson
Publisher: VST
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Chapter 7, Problem 50P
A particle with total energy 3.5 J is trapped in a potential well described by U = 7.0 − 8.0x + 1.7x2, where U is in joules and x in meters. Find its turning points.
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2.
A particle is trapped in a potential well described by U(x)= 1.9x2−b where U is in joules, x is in meters, and b = 2.6 J. Find the force on the particle when it's at x = 2.9 m.
If the potential energy of a particle is given by
U (r, y, 2) = –kry?2³,
find the force associated with this potential energy where k is a positive constant.
k(2x²yz³i+y²z³j + xy²2²k)
kry²2*(i + ĵ + k)
k(y²2³i + 2xyz³j + 3xy²2²k)
-kry 2*(i +j+ k)
33
3
k(y²2*i+ xyz°j +xy²2² k)
Chapter 7 Solutions
EBK ESSENTIAL UNIVERSITY PHYSICS, VOLUM
Ch. 7.1 - Suppose it takes the same amount of work to push a...Ch. 7.2 - Gravitational force actually decreases with...Ch. 7.3 - A bowling ball is tied to the end of a long rope...Ch. 7.4 - For which of the following systems is (1)...Ch. 7.5 - A bowling ball is tied to the end of a long rope...Ch. 7.6 - The figure shows the potential energy associated...Ch. 7 - Figure 7.14 shows force vectors at different...Ch. 7 - Is the conservation-of-mechanical-energy principle...Ch. 7 - Why cant we define a potential energy associated...Ch. 7 - Can potential energy be negative? Can kinetic...
Ch. 7 - If the potential energy is zero at a given point,...Ch. 7 - If the difference in potential energy between two...Ch. 7 - If the difference in potential energy between two...Ch. 7 - If conservation of energy is a law of nature, why...Ch. 7 - Determine the work you would have to do to move a...Ch. 7 - Now lake Fig. 7.15 lo lie in a vertical plane, and...Ch. 7 - Rework Example 7.1, now taking the zero of...Ch. 7 - Find the potential energy associated with a 70-kg...Ch. 7 - You fly from Bostons Logan Airport, at sea level,...Ch. 7 - How much energy can be stored in a spring with k =...Ch. 7 - How far would you have to stretch a spring with k...Ch. 7 - A biophysicist grabs the ends of a DNA strand with...Ch. 7 - A skier starts down a frictionless 32 slope. After...Ch. 7 - A 10,000-kg Navy jet lands on an aircraft carrier...Ch. 7 - A 120-g arrow is shot vertically from a bow whose...Ch. 7 - In a railroad yard, a 35,000-kg boxcar moving at...Ch. 7 - You work for a toy company, and youre designing a...Ch. 7 - A 54-kg ice skater pushes off the wall of the...Ch. 7 - Prob. 23ECh. 7 - A particle slides along the frictionless track...Ch. 7 - A particle slides back and forth on a frictionless...Ch. 7 - A particle is trapped in a potential well...Ch. 7 - Example 7.3: A climbing rope is designed to exert...Ch. 7 - Example 7.3: A climbing rope exerts a force given...Ch. 7 - Example 7.3: The force on an electron in an...Ch. 7 - Example 7.3: The potential energy of an electron...Ch. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Example 7.5: In a railroad switchyard, a rail car...Ch. 7 - Prob. 34ECh. 7 - The reservoir at Northfield Mountain Pumped...Ch. 7 - A carbon monoxide molecule can be modeled as a...Ch. 7 - A more accurate expression for the force law of...Ch. 7 - For small stretches, the Achilles tendon can be...Ch. 7 - A particle moves along the x-axis under the...Ch. 7 - As a highway engineer, youre asked to design a...Ch. 7 - A spring of constant k, compressed a distance x,...Ch. 7 - A child is on a swing whose 3.2-m-long chains make...Ch. 7 - With x x0 = h and a = g, Equation 2.11 gives the...Ch. 7 - The nuchal ligament is a cord-like structure that...Ch. 7 - A 200-g block slides back and forth on a...Ch. 7 - Automotive standards call for bumpers that sustain...Ch. 7 - A block slides on the frictionless loop-the-loop...Ch. 7 - The maximum speed of the pendulum bob in a...Ch. 7 - A mass m is dropped from height h above the top of...Ch. 7 - A particle with total energy 3.5 J is trapped in a...Ch. 7 - (a) Derive an expression for the potential energy...Ch. 7 - In ionic solids such as NaCl (salt), the potential...Ch. 7 - Repeat Exercise 19 for the case when the...Ch. 7 - As an energy-efficiency consultant, youre asked to...Ch. 7 - A spring of constant k = 340 N/m is used to launch...Ch. 7 - A bug slides back and forth in a bowl 15 cm deep,...Ch. 7 - A 190-g block is launched by compressing a spring...Ch. 7 - Prob. 58PCh. 7 - An 840-kg roller-coaster car is launched from a...Ch. 7 - Prob. 60PCh. 7 - A child sleds down a frictionless hill whose...Ch. 7 - A bug lands on top of the frictionless, spherical...Ch. 7 - A particle of mass m is subject to a force...Ch. 7 - A block of weight 4.5 N is launched up a 30...Ch. 7 - Your engineering department is asked to evaluate...Ch. 7 - Your roommate is writing a science fiction novel...Ch. 7 - You have a summer job at your universitys zoology...Ch. 7 - Biomechanical engineers developing artificial...Ch. 7 - Blocks with different masses are pushed against a...Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....Ch. 7 - Nuclear fusion is the process that powers the Sun....
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- Consider a particle moving in the region x > 0 under the influence of the potential where U0 = 1 J and α = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima.arrow_forwardA particle of mass 2.0 kg moves under the influence of the force F(x)=(3/x)N. If its speed at x=2.0 m is v=6.0 m/s, what is its speed at x = 7.0 m?arrow_forwardA mysterious force acts on all particles along a particular line and always points towards a particular point P on the line. The magnitude of the force on a particle increases as the cube of the distance from that point; that is Fr3 , if the distance from P to the position of the particle is r. Let b be the proportionality constant, and write the magnitude of the force as F=br3. Find the potential energy of a particle subjected to this force when the particle is at a distance D from P, assuming the potential energy to be zero when the particle is at P.arrow_forward
- A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance?arrow_forward(a) Can the kinetic energy of a system be negative? (b) Can the gravitational potential energy of a system be negative? Explain.arrow_forwardA block of mass 200 g is attached at the end of a massless spring of spring constant 50 N/m. The other end of the spring is attached to the ceiling and the mass is released at a height considered to be where the gravitational potential energy is zero. (a) What is the net potential energy of the block at the instant the block is at the lowest point? (b) What is the net potential energy of the block at the midpoint of its descent? (c) What is the speed of the block at the midpoint of its descent?arrow_forward
- Check Your Understanding What potential energy U(x) can you substitute in Equation 8.13 that will result in motion with constant velocity of 2 m/s for a particle of mass 1 kg and mechanical energy 1 J?arrow_forwardConsider a particle on which a force acts that depends on the position of the particle. This force is given by . Find the work done by this force when the particle moves from the origin to a point 5 meters to the right on the x-axis.arrow_forwardCheck Your understanding In Example 8.1 what are the potential energies of the particle at x=1 m and x=2 m with respect to zero at x=1.5 ?verify that the difference of potential energy is still 7 J.arrow_forward
- 247. Consider a particle moving in the region x> 0 under the influence of the potential a + а, U(x) %3D where U, = 1 J and a = 2 m. Plot the potential, find the equilibrium points, and determine whether they are maxima or minima.arrow_forwarda particle is moving under the potential V(x)=cx³-dx². Here c and d are constants. The particle is at rest initially and is at stable point. Calculate the minimum speed of the particle when it reached to unstable point.arrow_forwardA body with mass 0.40 kg moves in one dimension according to a potential of theform U(x) = A/x3-B/x , where A = 4.0 Jm3 abd B = 3.0 Jm, and we take x > 0. (a) If the speed of the body at x = 4.0m is v = 3.9 ms−1, what is the speed at x = 1.5 m? (b) Explain briefly what type(s) of motion are possible in this potential if the totalenergy E = 3.0 J.arrow_forward
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