The potential energy of a 4-kg object is given by U = 3x 2 x 3

Question:

The potential energy of a 4-kg object is given by U = 3x² − x³ for x ≤ 3 m, and U = 0 for x ≥ 3 m, where U is in joules and x is in meters.

(a) At what positions is this object in equilibrium?

(b) Sketch a plot of U versus x.

(d) If the total energy of the particle is 12 J, what is its speed at x = 2 m?

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Fundamentals of Ethics for Scientists and Engineers

ISBN: 978-0195134889

1st Edition

Authors: Edmund G. Seebauer, Robert L. Barry

See More Books

Question Posted: Jun 30, 2011 01:52 PM

See More Questions

The potential energy of a particle constrained to move along the x -axis is shown in the graph. At x = 0, the particle is moving in the + x -direction with a kinetic energy of 200 J. Can this...
The potential energy of a particle constrained to move along the x -axis is shown in the graph. At x = 0, the particle is moving in the + x -direction with a kinetic energy of 400 J. Can this...
The potential energy of a diatomic molecule (a two-atom system like H2 or O) is given by where r is the separation of the two atoms of the molecule and A and B are positive constants. This potential...
Maria is opposed to the idea of same-sex marriage. In a recent conversation in the school cafeteria, Maria argues, "If homosexuals are allowed to marry, then why not allow polygamy or other kinds of...
What sort of demand management techniques would an exclusive restaurant use when demand exceeds their capacity? What about McDonalds? Discuss.
The following selected transactions were completed by Epic Co. during August of the current year: Aug. 3. Purchased merchandise on account for $33,400, terms FOB destination, 2/10, n/30. 9. Issued...
This assignment begins with a completed simulation of the toluene hydrodealkylation process in Figure 17.1 and involves the completion of an economic evaluation. Note that the simulation results for...
A company retired $60 million of its 6% bonds at 102 ($61.2 million) before their scheduled maturity. At the time, the bonds had a remaining discount of $2 million. Prepare the journal entry to...
A car runs on wheels of diameter 3 5 0 mm . The car is travelling at an average speed of 7 5 km / h , what is the angular velocity of the wheels?
Kevin is the owner of Flyties Pty Ltd. He has just built a large, state-of-the-art indoor skydiving arena. Kevin organises a competition where entrants compete to see who can complete the most...
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 at these points U(x) is a local maximum or minimum, respectively.
A force is given by F x = Ax -3 , where A = 8 Nm 3 . (a) For positive values of x, does the potential energy associated with this force increase or decrease with increasing x? (You can determine the...
Mossfort, Inc., has a division in Canada that makes long-lasting exterior wood stain. Mossfort has another U.S. division, the Retail Division, that operates a chain of home improvement stores. The...
Let $I=\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$, where \[ \mathbf{F}(x, y, z)=\left\langle\frac{2 y z}{r^{2}},-\frac{x z}{r^{2}},-\frac{x y}{r^{2}}ightangle \]...
Show that $\operatorname{curl}(\mathbf{F})=\mathbf{0}$ if $\mathbf{F}$ is radial, meaning that $\mathbf{F}=f(ho)\langle x, y, zangle$ for some function $f(ho)$, where...
Use the Divergence Theorem to evaluate the flux $\iint_{\mathcal{S}} \mathbf{F} \cdot d \mathbf{S}$. $\mathbf{F}(x, y, z)=\left\langle x^{2} z, y x, x y zightangle, \mathcal{S}$ is the boundary...
Explain briefly how auditing techniques have been affected by: (i) growth in the size of companies (ii) changes in technology.
Suppose that a nation has implemented a system for applying a tax rate of 2 percent to the incomes earned by the 10 percent of its residents with the highest incomes. All funds collected are then...
Solve the differential equation in problem 8 for the following boundary conditions using the Galerkin method: Assume the approximate solution as: where $\phi_{0}(x)$ is a function that satisfies...
The May 2014 revenue and cost information for Houston Outfitters, Inc. follow: Sales Revenue (at standard).............. $ 540,000 Cost of Goods Sold (at standard) ..........341,000 Direct Materials...
(a) Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber,...
In Figure P30.17, the current in the long, straight wire is I1 = 5.00 A and the wire lies in the plane of the rectangular loop, which carries the current I2 = 10.0 A. The dimensions are c = 0.100 m,...
Two long, parallel wires are attracted to each other by a force per unit length of 320 N/m when they are separated by a vertical distance of 0.500 m. The current in the upper wire is 20.0 A to the...
Three long wires (wire 1, wire 2, and wire 3) hang vertically. The distance between wire 1 and wire 2 is 20.0 cm. On the left, wire 1 carries an upward current of 1.50 A. To the right, wire 2 carries...
There are two real numbers a for which (2x)+15 (1-x) = 8x - 3x + 2. The sum of these two real numbers is
Net sales Cost of goods sold Depreciation INCOME STATEMENT (Figures in $ millions) Earnings before interest and taxes (EBIT) Interest expense Income before tax Taxes Net income $ 882.00 742.00 32.00...
Venita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and t length of the row. Sewing Number of Length (cm) stitches 5 1 15 3 20 4 30 6 What is...

The potential energy of a 4-kg object is given by U = 3x 2 x 3

Question:

Step by Step Answer:

a Proceed as in Problem 668 dUdx 3x2 x 0 For x 0 2 m Also for x ...View the full answer

Fundamentals of Ethics for Scientists and Engineers

Students also viewed these Mechanics questions