None Figure 1 shows the potential energy associ-ated with a conservative force F(x).1. A particle of mass m₁ = 1 kg is undergo-ing F(x) and no other forces. The me-chanical energy of the system is 9 J.(a) What is the sign of the force as afunction of x?(b) Where are the turning points of thesystem (if any)?(c) where are the equilibrium pointsof the system (if any)? are theystable?U (J)1086420246810x (m)Figure 1: Potential energy of a conservative(d) what is the velocity of the particle force F(x).at x = 4m?2. Describe the motion of a second particle of mass m2=2 kg with initial velocity vo=-1 ms¹ and initial position xo=3 m.

Step 1: Analyzing the Force Direction:Examine the potential energy curve provided in the figure.…

Answered: Figure 1 shows the potential energy…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter6: Energy Of A System

Section: Chapter Questions

Problem 8CQ

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“ E=K+Uconstant is a special case of the work energy theorem.” Discuss this statement.
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?
A particle of mass 0.50 kg moves along the x -axis with a potential energy whose dependence on x is shown below. (a) What is the force on the particle at x = 2.0, 5.0, 8.0, and 12 m? (b) If the total mechanical energy E of the particle is —6.0 J, what are the minimum and maximum positions of the particle? (c) What are these positions if E = 2.0 J? (d) If E = 16 J, what are the speeds of the particle at the positions listed in part (a)?
A 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.
An electron in a television tube is accelerated uniformly from rest to a speed of 8.4107 m/s over a distance of 2.5 cm. What is the power delivered to the electron at the instant that its displacement is 1.0 cm?
Two bodies are interacting by a conservative force Show that the mechanical energy of an isolated system consisting of two bodies interacting with a conservative force is conserved. (Hint: Start by using Newton’s third law and the definition of work to find the work done on each body by the conservative force.)
A person in good physical condition can put out 100 W of useful power for several hours at a stretch, perhaps by pedaling a mechanism that drives an electric generator. Neglecting any problems of generator efficiency and practical considerations such as resting time: (a) How many people ‘would it take to nm a 4.O0-kW electric clothes dryer? (b) How many people would it take to replace a large electric power plant that generates 800 MW?
Consider a linear spring, as in Figure 7.7(a), with mass M uniformly distributed along its length. The left end of the spring is fixed, but the right end, at the equilibrium position x=0 , is moving with speed v in the x-direction. What is the total kinetic energy of the spring? (Hint: First express the kinetic energy of an infinitesimal element of the spring dm in terms of the total mass, equilibrium length, speed of the right-hand end, and position along the spring; then integrate.)
In a Coyote/Road Runner cartoon clip (https://openstaxcollege.org/l/21coyroadcarcl), a spring expands quickly and sends the coyote into a rock. If the spring extended 5 m and sent the coyote of mass 20 kg to a speed of 15 m/s, (a) what is the spring constant of this spring? (b) If the coyote were sent vertically into the air with the energy given to him by the spring, how high could he go if there were no non-conservative forces?
Check Your Understanding The spring Example 7.5 is compressed 6 cm from its equilibrium length. (a) Does the spring force do positive or negative work and (b) what is the magnitude?
A 200-g steel ball is tied to a 2.00m “massless” string and hung from the ceiling to make a pendulum, and then, the ball is brought to a position making a 30 angle with the vertical direction and released from rest. Ignoring the effects of the air resistance, find the speed of the ball when the string (a) is vertically down, (b) makes an angle of 20 with the vertical and (c) makes an angle of 10 with the vertical.
A particle of mass 4.0 kg is constrained to move along the x -axis under a single force F(x)=cx3 , where c=8.0N/m3 . The particle’s speed at A, where xA=1.0m , is 6.0 m/s. What is its speed at B, where xB=2.0m ?

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