The force on a particle is described by 2x3 - 4 at a point æ along the a-axis. Find the work done in moving the particle from the origin to x = 3.

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 force on one end of a parabolic trough full of water if the depth is 2 feet and the width…

A:

Q: The 110-lb force P is applied to the 200-lb crate, which is stationary before the force is applied.…

A:

Q: Find the work done when a constant force F =14 lbs moves a chair from x =2.9 to x =3.6 ft. along the…

A:

Q: How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N…

A: given How much work does it take to slide a crate 20 m along a loading dock by pulling on it with 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: The figure to the right shows the shape and dimensions of a small dam. Assuming the water level is…

A:

Q: Find the work done when a constant force F =16 lbs moves a chair from x =2.4 to x =5.1 ft. along the…

A:

Q: The body on the ( 30°) incline is acted upon by a force (P) inclined at ( 20° ) with the horizontal.…

A: According to question,θ=20°+30°   = 50°Perpendicular component,Pn=300 tan θ     =300 tan 50°     =…

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: Suppose that 2J of work is needed to stretch a spring from it’s natural length of 30 cm to a length…

A: Given:The original length of the spring is 30 cm.The work done to stretch the spring from 30 cm to…

Q: Find the work done by the force F = 7i - 3j in moving an object from the point (2, 2) to the point…

A:

Q: Find the work done when a constant force F =11 lbs moves a chair from x =2.4 to =4.6 ft. along the…

A: In this question we have to find work done.

Q: Find the acute angle that a constant unit force vector makes with the positive x-axis if the work…

A: Given- a constant unit force vector makes with the positive x-axis if the work done by the force in…

Q: Find the work done by a force F = −3j pounds applied to a point that moves on a line from (1, 3) to…

A: Given: F=-3j

Q: Approximate the change in the magnitude of the electrostatic force between two charges when the…

A: Magnitude is the size or numerical quantity or value. The approximation change formula is ∆y=f'(a)∆x…

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: Suppose you apply a force of 80 N to a 0.25-meter-long wrench attached to a bolt in a direction…

A: This question is related to vector,  directions, magnitude and torque calculations. We will solve it…

Q: A 20-lb force is applied to the control rod AB as shown. Knowing that the length of the rod is 9 in.…

A:

Q: A 12.0-kg box (m,) is connected to an empty 2.00-kg bucket (m2) by a cord running over a very light…

A:

Q: F= (e* – y+ xcosh(x))i+ (y³/2 + x)j.

A:

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

A: Given; F=xyi +(y-x)j.

Q: Find the force on one end of a parabolic trough full of water, if the depth is 2 ft. and width…

A: Given that the depth of the parabolic trough is 2 ft and width across the top 2 ft. The objective is…

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

A:

Q: Find the work done by a force of 14i (newtons) in moving as object along a line from the origin to…

A: Work done is given by the product of Force and displacement. That is: W=F×dwhere F is force and d is…

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

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Q: Find the work W done by a force of 7 pounds acting in the direction 30° to the horizontal in moving…

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Q: 3. A wagon is pulled a distance of 48 metres by a force of 30N applied at an angle of 51° to the…

A:

Q: The figure to the right shows the shape and dimensions of a small dam. Assuming the water level is…

A: Given density 1000kg/m^3, acceleration due to gravity 9.8 m/s^2

Q: Find the work done in pushing a car along a level road from point A to point B, 80 feet from A,…

A: Given: F=95 pounds, d=80feet we know that workW is given by W=F.d…

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: A cylindrical tank half full of water is lying on its side. If the radius of the tank is 1m and the…

A: Let the density of the water be w And the total height including the strip be μ Let us assume that…

Q: If the magnitude of the resultant force is to be 9 kN directed along the positivex axis determine…

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Q: A kid pulls a wagon with a force of 26 N at an angle of 62° to the ground.  How much work is…

A: We have, A kid pulls a wagon with a force of 26 N at an angle of 62° to the ground. Now, component…

Q: Ojemba is sitting on a sled on the side of a hill inclined at 60 degrees. The combined weight of…

A: The combined weight as: F=0,-160, since gravity acts vertically downward. Also, the side of the hill…

Q: Find the work done (in ft-Ilb) when a constant force F = 17 lb moves a chair from x = 0.2 to x = 1.8…

A:

Q: Suppose that an object moves in the positive direction along a coordinate line while subjected to a…

A: Using formula for work done

Q: 1) Find -(d(PE))/dx in order to find the force acting on the object. (from the equation…

A: Formula:

Q: Find the work done in pushing a car along a level road from point A to point B, 93 feet from A,…

A:

Q: A plate shaped like an isosceles triangle with a height of 1 m is placed on a vertical wall 1 m…

A:

Q: A 500-pound boat sits on a ramp inclined at 45°. What is the force required to keep the boat from…

A: This is a problem of vector calculus.

Q: A tractor pulls a log 800 meters up a hill with a grade of 4%. The force on the cable connecting he…

A: Solution Given  A Tractor pulls a log 800 meter up a hill with a grade of 4%. The force on the cable…

Q: A particle is accelerated along a curved path of lengthl = 4.0 m under the action of an applied…

A:

Q: A door is swung open by applying a 60 N force as shown, 2.0 m from the hinges. 2.0 m 100° 60 N ←--…

A: We have to find the torque applied at the hinge of the door.

Q: Determine the force being experienced by a 2-microcoulomb charge at (-2,4,6) m due to another point…

A:

Q: Find the work done if a force of F-4i + 7j Newtons moves an object from point A(-9,0) to the point…

A: Here we have to find the work done. The solution is following.

Q: If a constant force of 5 lb moves an object 10 ft, then the work done by the force on the object is…

A: we know that work done W by a constant force F to move a object to displacement of D is given as…

Q: The magnitude of the torque t developed by applying a force F at a point with position vector r at…

A: First we have to complete the required step by using the correct expression for torque.

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: Determine the required magnitude of force F if the resultant couple moment on the frame is 200 N-M,…

A: We will find the value of  F ,

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.