Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
4th Edition
ISBN: 9780134110684
Author: Randall D. Knight (Professor Emeritus)
Publisher: PEARSON
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Chapter 10, Problem 57EAP
- A system has potential energy
U(x) = x + sin ((2 rad/m)x)
as a particle moves over the range 0 m
- Where are the equilibrium positions in this range?
- For each, is it a point of stable or unstable equilibrium?
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A particle moves in one dimension (along the x-axis), where the potential energy is given by the function U(x) shown below. The constants are A = 2.00 J/m2 and B = 4.00 J/m. The total energy of the particle is E = 8.00 J.
U(x) = Ax2 + Bx
(a) What is the equilibrium position of the particle (x, in units of meters)? Is the equilibrium position stable or unstable?
(b) What range of positions is the particle restricted to? Give both xmin (the smallest possible position) and xmax (the largest possible position), in units of meters. Hint: the particle is restricted to move in the region where E ≥ U(x).
A particle moves in one dimension (along the x-axis), where the potential energy is given by the function U(x) shown below. The constants are A = 2.00 J/m2 and B = 4.00 J/m. The total energy of the particle is E = 8.00 J.
U(x)= Ax2+Bx
A) What is the equilibrium position of the particle (x, in units of meters)? Is the equilibrium position stable or unstable?
B) What range of positions is the particle restricted to? Give both xmin (the smallest possible position) and xmax (the largest possible position), in units of meters. Hint: the particle is restricted to move in the region where E ≥ U(x).
A particle with mass 2.5 kg is moving in one dimension subject to a potential energy function that is a 4th-order polynomial. There are equilibrium points at x= −2 m, x= 1 m, and x= 3 m. The potential energy is zero at the origin. When the particle is located at x = −2 m, it has a potential energy of 19.0 J and is moving with a speed of 5.0 m/s. What is the speed of the particle when it is located at x= 2 m?
Chapter 10 Solutions
Physics for Scientists and Engineers: A Strategic Approach, Vol. 1 (Chs 1-21) (4th Edition)
Ch. 10 - Prob. 1CQCh. 10 - Can kinetic energy ever be negative? Can...Ch. 10 - Prob. 3CQCh. 10 - 4. The three balls in FIGURE Q1O.4, which have...Ch. 10 - Rank in order, from most to least, the elastic...Ch. 10 - 6. A spring is compressed 1.0 cm. How far must you...Ch. 10 - Prob. 7CQCh. 10 - A particle with the potential energy shown in...Ch. 10 - A compressed spring launches a block up an...Ch. 10 - 10. A process occurs in which a system’s potential...
Ch. 10 - A process occurs in which a system’s potential...Ch. 10 - FIGURE Q10.12 is the energy bar chart for a...Ch. 10 - Prob. 13CQCh. 10 - Object A is stationary while objects B and C are...Ch. 10 - Prob. 2EAPCh. 10 - 3. The lowest point in Death Valley is 85 m below...Ch. 10 - Prob. 4EAPCh. 10 - Prob. 5EAPCh. 10 - 6. What height does a frictionless playground...Ch. 10 - 7. A 55 kg skateboarder wants to just make it to...Ch. 10 - Prob. 8EAPCh. 10 - A pendulum is made by tying a 500 g ball to a...Ch. 10 - A 20 kg child is on a swing that hangs from...Ch. 10 - A 1500 kg car traveling at 10 m/s suddenly runs...Ch. 10 - Prob. 12EAPCh. 10 - A cannon tilted up at a 30° angle fires a cannon...Ch. 10 - In a hydroelectric dam, water falls 25 m and then...Ch. 10 - How far must you stretch a spring with k = 000 N/m...Ch. 10 - A stretched spring stores 2.0 J of energy. How...Ch. 10 - A student places her 500 g physics book on a...Ch. 10 - A block sliding along a horizontal frictionless...Ch. 10 - A 10 kg runaway grocery cart runs into a spring...Ch. 10 - As a 15,000 kg jet plane lands on an aircraft...Ch. 10 - The elastic energy stored in your tendons can...Ch. 10 - The spring in FIGURE EX10.22a is compressed by ?x....Ch. 10 - The spring in FIGURE EXIO.23a is compressed by ?x....Ch. 10 - FIGURE EX10.24 is the potential-energy diagram for...Ch. 10 - Prob. 25EAPCh. 10 - In FIGURE EX10.26, what is the maximum speed of a...Ch. 10 - Prob. 27EAPCh. 10 - FIGURE EX10.28 shows the potential energy of a 500...Ch. 10 - In FIGURE EX10.28, what is the maximum speed a 200...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A system in which only one particle can move has...Ch. 10 - A particle moving along the y-axis is in a system...Ch. 10 - A particle moving along the x-axis is in a system...Ch. 10 - FIGURE EX10.34 shows the potential energy of a...Ch. 10 - A particle moves from A to D in FIGURE EX10.35...Ch. 10 - A force does work on a 50 g particle as the...Ch. 10 - A system loses 400 J of potential energy. In the...Ch. 10 - What is the final kinetic energy of the system for...Ch. 10 - How much work is done by the environment in the...Ch. 10 - A cable with 20.0 N tension pulls straight up on a...Ch. 10 - A very slippery ice cube slides in a vertical...Ch. 10 - A 50 g ice cube can slide up and down a...Ch. 10 - You have been hired to design a spring-launched...Ch. 10 - It’s been a great day of new, frictionless snow....Ch. 10 - Prob. 45EAPCh. 10 - A 1000 kg safe is 2.0 m above a heavy-duty spring...Ch. 10 - You have a ball of unknown mass, a spring with...Ch. 10 - Sam, whose mass is 75 kg, straps on his skis and...Ch. 10 - A horizontal spring with spring constant 100 N/m...Ch. 10 - Truck brakes can fail if they get too hot. In some...Ch. 10 - Prob. 51EAPCh. 10 - Use work and energy to find an expression for the...Ch. 10 - Prob. 53EAPCh. 10 - The spring shown in FIGURE 10.54 is compressed 50...Ch. 10 - Prob. 55EAPCh. 10 - Prob. 56EAPCh. 10 - A system has potential energy U(x) = x + sin ((2...Ch. 10 - Prob. 58EAPCh. 10 - Prob. 59EAPCh. 10 - Prob. 60EAPCh. 10 - The potential energy for a particle that can move...Ch. 10 - A particle that can move along the x-axis...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - An object moving in the xy-plane is subjected to...Ch. 10 - Prob. 65EAPCh. 10 - In Problems 66 through 68 you are given the...Ch. 10 - Prob. 67EAPCh. 10 - Prob. 68EAPCh. 10 - A pendulum is formed from a small ball of mass m...Ch. 10 - Prob. 70EAPCh. 10 - Prob. 71EAPCh. 10 - Prob. 72EAPCh. 10 - The spring in FIGURE CP10.73 has a spring constant...Ch. 10 - A sled starts from rest at the top of the...
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