A particle is moved along the x-axis by a force F(x) = x² + 5x – 6 . How much work is done in moving the particle from x = -2 to x = 4?

Q: 9. Suppose that 2 J of work is needed to stretch a spring from its natural length of 30 cm to a…

A:

Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

A: Stretched distance = 42-30 =12  cm = 0.12 m  Let F=kx [ by Hooke's law ]  So,

Q: Find the work required to compress a spring from its natural length of1 ft to a length of 0.75 ft if…

A:

Q: A particle of mass m is moving under the force of attraction of another particle of mass m1 at a…

A: When a force F is applied to an object of mass m, the position of body changes. According to…

Q: Find the work done by the force F = xyi + (y - x)j over the straight line from (1,- 2) to (2, - 4).

A:

Q: How much work is required to move an object from x=4 to x =11 (measured in meters) in the presence…

A:

Q: 10. What is the work done moving a particle from x = 0 to x = 1 m if the force acting on it is F =…

A:

Q: Find the work done by a force F = 5i (mag-nitude 5 N) in moving an object along the line from the…

A: Given,

Q: 6: Find the work done by the force F = -7y i+ 10x j along one loop of the curver = sin 70 (in the…

A: Given

Q: A body of mass m falls from the rest in a medium offering resistance proportional to the square of…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: A shell of mass 5 kg is shot upward with an initial velocity of 250 m/sec. The magnitude of the…

A: The equilibrium of a body is considered as the state of the body when there is no force acting on a…

Q: Find the work done by the force field

A: Given: The given function is, With A(1,1) and B(4,4). To find: The work done by the force field F…

Q: Calculate the work done by a constant force field F on a particle that moves once uniformly along…

A: Given, path of the curve x^2+y^2=1 & F(x,y)=(αx,αy)

Q: (True/False) Suppose the work done by a force F on a particle moving along a path C is given by x,…

A: True.

Q: Find the work done by a force F of 12 pounds acting in the direction (3,1) in moving an object 8…

A:

Q: Find the work done under the influence of the force E = 3xyi – 5zj + 10xk along the curve x= t² + 1,…

A:

Q: Use the differential dz to approximate the change in z = √4 − x2 − y2 as (x, y) moves from the point…

A:

Q: A force with magnitude 35 N acts directly upward from the xy-plane on an object with mass 7 kg. The…

A:

Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

A: Let the force to hold the spring at a distance x beyond the natural length x is = f(x)=kx For 40 cm,…

Q: Find the work done by the force F =xyi + (y - x)j over the straight line from (- 2, - 1) to (-1,0).

A:

Q: It took 1800 J of work to stretch a spring from its natural length of 2 m to a length of 5 m. Find…

A:

Q: Find the potential function for F(x,y,z) = (x^-1z)i + (y^-1z)j + ln(xy)k. Show all steps and explain

A: Potential function of  F, is f such that ∇f=F.

Q: 2 5. x = 1+t2 2 y= t(1+t?)

A:

Q: Suppose that 4 Joules of work is needed to stretch a spring from its natural length of 11 cm to a…

A:

Q: A force F(x) = 10−2x N applied in the positive x-direction moves an object 3m from x = 2to x = 5.…

A: Given that , Fx=10-2x N Work (W)=?

Q: Find the work done by the force F = xyi + (y-x)j over the straight line from (0,0) to (1, - 3). The…

A:

Q: Which of the following is the work done by a constant force F moving an object along a straight line…

A: The work done is defined as the integral of the force F with respect to the distance.   The work…

Q: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

A: Given: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

Q: Find the total differential. 2x + y W = 5z - 4y

A: For a function of two or more independent variables, the total differential of the function is the…

Q: Find the work done for a force F = N from x =2 to x =3 m. x2

A:

Q: Show that whether if the co-vector w can be written as dø differential? w = y. (x +). dx + x. (+).dy…

A: Given:  w=y·x+y2· dx+x·x2+y·dy....(1)

Q: Find the work done when a constant force F=16l bs moves a chair from x =2.4 to x =3.1 ft. along the…

A: Solve the following

Q: EX 3! Show that F (x₁y) = (2xy - 3) + " + (2y + x² ) 5* is conservative and find a potential of it..

A: Use the partial derivative for finding the potential function

Q: You have been asked to find the path along which a force field F will perform the least work in…

A:

Q: Assume that a body moving with velocity v encounters resistance of the form dv/dt = -kv3/2. Show…

A:

Q: Find the differential of f(x, y) = Væ² +y8 at the point (1, 3). df = Then use the differential to…

A:

Q: A particle moves through 3-space in such a way that its acceleration is a(t) = 8 sin 2ti + 8 cos…

A: Gg

Q: 2. u(x)= secx+à So u(1)dt.

A:

Q: Find the work done by the force F (x; y) = xyi-(y-x)j over the straight line from (1,1) to (2,3)

A:

Q: Suppose that an object moves in the positive direction along a coordinate line over the interval [a,…

A: Let the object moves in the positive direction along a coordinate line over the interval [a, b] Let…

Q: It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 4 m. Find…

A:

Q: Q7) The work done by the force F = 2j to move a particle from the origin to the point (3,3,3) is:

A:

Q: he position x(t) of an object moving in 1-D on the a - aris in an inverse-square force held (such as…

A: As given by the question There are given that the equation of inverse-square force field is:…

Q: Consider a beam of length 10m and negligible mass, modelled as a rigid body in the x-direction from…

A: Here I am attaching image so that you understand each and every step.

Q: Find the work done for a force F 36 N from x =2 to x =6 m. %3D

A: Here we have to find the work done by the given force on the given interval. Here we use integration…

Q: 3. A particle is located at a distance x meters from the origin, a force of x +2 newtoms is acting…

A: To find the work done

Q: Use computer software to obtain a direction field for the given differential equ y' = x (a) y(0) = 0

A: Given the differential equation is            y'=x

Q: How much work is required to move an object from x = 1 to x = 3 (measured in meters) in the presence…

A: The function f(x)=2x2. N moves an object from x = 1 to x = 3. We have to find work required to move…

Q: Find the work done by the force F(r) = x2 +1 in moving a particle along the T-axis from r = 0 to r…

A: The work done by a variable force F(x) in moving a particle along the x-axis is given by the…