Question: The force acting on an object is given by F(x) = x 3 4x. Locate the positions of unstable and stable equilibrium and show that

The force acting on an object is given by F(x) = x³ 4x. Locate the positions of unstable and stable equilibrium and show that at these points U(x) is a local maximum or minimum, respectively.

Step by Step Solution

★★★★★

3.45 Rating (165 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Fx xx 2 4 Fx 0 at x 0 2 At x 0 A small increase in x makes ... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

10-P-M-W-E (281).docx

120 KBs Word File

Students Have Also Explored These Related Mechanics Questions!

The force acting on an object is given by F x = a/x 2 . Determine the potential energy of the object as a function of x.

The net force acting on an object is constant. Under what circumstances does the object move along a straight line? Under what circumstances does the object move along a curved path?

The speed, v of an object is given by the equation v = At3 Bt, where t refers to time. What are the dimensions of A and B?

1. b) Most problems in introductory physics present a situation and ask you to determine what will happen next using ideas that were just introduced. For example, determining the force on a specic...

7. A satellite of mass 120 kg is in circular orbit at a height h = R above the surface of Earth, where R is the radius of Earth. The radius and mass of Earth are 6.4 x 10" m and 6.0 x 10" kg,...

Please I need help with the questions for Calculations (Part ), Calculations (Part 2), the graph, and questions 1-2 on the last page. THE DATA TO DO THE CALCULATIONS ARE PROVIDED IN THE TABLES. THATS...

12. [-I1 Points] DETAILS SERPSE10 7.A.OP.030. 0/6 Submissions Used MY NOTES ASK YOUR TEACHER A person throws a 0.150 kg ball with a speed of 37.6 m/s at an angle of 29.0" to the horizontal. Calculate...

I need help with this lab. Please answer questions for pages 4-7. Freefall Purpose: We will measure the value of 'little g', or the acceleration due to gravity on the surface of Earth. The particular...

1. [0/2 Points] DETAILS PREVIOUS ANSWERS OSCOLPHYS2016ACC 8.1.P.004. (a) What is the momentum in kg . m/s of a garbage truck that is 1.10 x 10" kg and is moving at 34.0 m/s? (Enter a number.) 340000...

Please help with these physics questions! 1) A fully loaded Boeing 747 with all engines at full thrust accelerates at 2.6 m/s2. Its minimum takeoff speed is 70 m/s. Here, suffices i and f represent...

4. (20 points) Difference Equations (a) (5 points) A bank account accrues with an interest rate r per year. It has no deposits or withdrawals after time n = 0. What is the difference equation for...

Access the following 3 sources and respond to the requirements: Your state board of professional counseling website (Virginia State Board of professional counseling). Once you have found the website,...

6-10 What is compound interest?

A ships roll can be stabilized with a control system. A voltage applied to the fins actuators creates a roll torque that is applied to the ship. The ship, in response to the roll torque, yields a...

Corporate Social Responsibility. Methamphetamine (meth) is an addictive drug made chiefly in small toxic labs (STLs) in homes, tents, barns, and hotel rooms. The manufacturing process is dangerous,...

Write an application with three check boxes labeled Red, Green, and Blue that adds a red, green, or blue component to the background color of a panel in the center of the frame. This application can...

Presented below is the adjusted trial balance of Abbey plc at December 31, 2022. Additional information: 1. Net loss for the year was 2,500. 2. No dividends were declared during 2022. Instructions...

Given the two networks shown, find the Y parameters for the circuit in (a) and Z parameters for the circuit in (b).

(a) An oxygen-16 ion with a mass of 2.66 x 10 -26 kg travels at 5.00 x 10 6 m/s perpendicular to a 1.20-T magnetic field, which makes it move in a circular arc with a 0.231-m radius. What positive...

Determine the magnetic field (in terms of I, a, and d) at the origin due to the current loop in Figure P30.14. 0 t a

Two long, parallel conductors carry currents I1 = 3.00 A and I2 = 3.00 A, both directed into the page in Figure P30.15. Determine the magnitude and direction of the resultant magnetic field at P. ...

Two long, parallel conductors, separated by 10.0 cm, carry currents in the same direction. The first wire carries current I1 = 5.00 A and the second carries I 2 = 8.00 A. (a) What is the magnitude of...

Assume that you have been given the following financial statement data (in $ millions) for KRJ Corporation. Note that all data are represented in absolute value terms and that not all of the...

The American Opportunity Credit is characterized by all of the following EXCEPT: It can be claimed only for the first four years of a post - secondary education The maximum annual credit amount is $...

{a} Find tom when it = 9. {b} Find tU_025 when 1:216. (cl Find 1030 when 1: =13. Click here to View:r age 1 of the table of critical values of the tdistributien. Click here to View:r age 2 of the...