A clever engineer designs a "sprong" that obeys the force law Fx=−q(x−xe)3, where xe is the...
A clever engineer designs a "sprong" that obeys the force law Fx=−q(x−xe)3, where xe is the equilibrium position of the end of the sprong and q is the sprong constant. For simplicity, we'll let xe=0m. Then Fx=−qx3. Find an expression for the potential energy of a stretched or compressed sprong.
Homework Answers
from the relation between force and potential energy
f = -du/dx
u = -
fdx
u = qx^3 dx
u = q(x^4/4)
u = 1/4*qx^4
Add Answer to:
A clever engineer designs a "sprong" that obeys the force law
Fx=−q(x−xe)3, where xe is the...
Because of your role in the 'Great Penguin Riot and Massacre of 2014,' you have been...
Because of your role in the 'Great Penguin Riot and Massacre of 2014,' you have been relegated to the slug pen. While attending to your many exciting responsibilities, you have had time to design a new thingamajig which you can call a sprong. After months of careful testing, you have determined that the spring obeys the force law F=-q (x-xe)^3î-q (y-ye)^3j where xe and ye are the equilibrium positions for the x-coordinate and ya coordinate, respectively. For simplicity, let xe=0...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
2. Consider the following physical situation: A spring that obeys Hooke's Law and has a known/given spring constant k has been compressed to half of its equilibrium length. It's anchored at o...
2. Consider the following physical situation: A spring that obeys Hooke's Law and has a known/given spring constant k has been compressed to half of its equilibrium length. It's anchored at one end while the other end pushes (but is not attached to) a block of mass m in the horizontal direction. The block is initially held in place. Once released, the block accelerates to the right and achieves a final speed of ve at the point when it leaves...
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position....
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position. The spring is then released and stretched by 5.0 ㎝ from its equilibrium position. Find the difference in potential energy between the two positions of the spring (stretched and compressed).
A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x)N where x is...
A particle that can move along the x-axis experiences an interaction force Fx=(3x2−5x)N where x is in m. Find an expression for the system's potential energy. Express your answer in terms of the variables x and the constant of integration C, where C is in joules.
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is req...
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.5 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in jo...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
1a. 1b. 1c. A single conservative force = (AX - B) N, where x is in...
1a.
1b. 1c.
A single conservative force = (AX - B) N, where x is in meters, and A and B are positive constants, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 0 at x = 0. (a) Write an expression for the potential energy associated with this force. (b) What is the maximum positive value of the potential energy? In the figure, a block of...
A spring is found to not obey Hooke's law. It exerts a restoring force F(x) =-ax-...
A spring is found to not obey Hooke's law. It exerts a restoring force F(x) =-ax- 2 N if it stretched or compressed, where α = 60 N/m and β 18.0 Nm2/3. The mass of the spring is negligible. (a) Calculate the work function W(x) for the spring. Let U=0 when x=0. (b) An object of mass 0.900 kg on a horizontal surface is attached to this spring. The surface provides a friction force that is dependent on distance Fr(x)2x2...
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x)...
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x) = Fosin (cx), where F. = 2 N and c = 0.5 rad/m are constants (a) Prove that this force is conservative. (b) Find the potential energy function V(x) (c) Make a graph of the potential energy V(x) as a functions of x in the interval [x = -a m,x = + m) d) Us previous graph to discuss the motion of the particle...
Consider a mass m suspended from a massless spring that obeys Hooke's Law (i.e. the force required to stretch or compress it is proportional to the distance stretched/compressed). The kinetic energy T of the system is mv2/2, where v is the velocity of the mass, and the potential energy V of the system is kr-/2, where k is the spring constant and x is the displacement of the mass from its gravitational equilibrium position. Using Lagrange's equations for mechanics (with...
2. Consider the following physical situation: A spring that obeys Hooke's Law and has a known/given spring constant k has been compressed to half of its equilibrium length. It's anchored at one end while the other end pushes (but is not attached to) a block of mass m in the horizontal direction. The block is initially held in place. Once released, the block accelerates to the right and achieves a final speed of ve at the point when it leaves...
A spring of force constant 3 N/m is compressed by 5.0 em from its equilibrium position. The spring is then released and stretched by 5.0 ㎝ from its equilibrium position. Find the difference in potential energy between the two positions of the spring (stretched and compressed).
Suppose a force of 40 N is required to stretch and hold a spring 0.1 m from its equilibrium position. a. Assuming the spring obeys Hooke's law, find the spring constant k. b. How much work is required to compress the spring 0.2 m from its equilibrium position? c. How much work is required to stretch the spring 0.5 m from its equilibrium position? d. How much additional work is required to stretch the spring 0.1 m if it has...
3) Consider Hooke's Law: The force required to keep a spring in a compressed or stretched position x units from the spring's equilibrium position is F(x)-kr Calculate the work required, in joules, to stretch a spring 0.4 meters beyond its equilibrium position for each of the following scenarios. a) The spring requires 50 Newtons of force to hold it 0.1 m from its equilibrium position. b) The spring requires 2 Joules of work to stretch the spring 0.1 meter from...
1a.
1b. 1c.
A single conservative force = (AX - B) N, where x is in meters, and A and B are positive constants, acts on a particle moving along an x axis. The potential energy U associated with this force is assigned a value of 0 at x = 0. (a) Write an expression for the potential energy associated with this force. (b) What is the maximum positive value of the potential energy? In the figure, a block of...
A spring is found to not obey Hooke's law. It exerts a restoring force F(x) =-ax- 2 N if it stretched or compressed, where α = 60 N/m and β 18.0 Nm2/3. The mass of the spring is negligible. (a) Calculate the work function W(x) for the spring. Let U=0 when x=0. (b) An object of mass 0.900 kg on a horizontal surface is attached to this spring. The surface provides a friction force that is dependent on distance Fr(x)2x2...
Q.3) (7 Marks An object of mass m is being acted upon by a force F(x) = Fosin (cx), where F. = 2 N and c = 0.5 rad/m are constants (a) Prove that this force is conservative. (b) Find the potential energy function V(x) (c) Make a graph of the potential energy V(x) as a functions of x in the interval [x = -a m,x = + m) d) Us previous graph to discuss the motion of the particle...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago