Find the acute angle that a constant unit force vector makes with the positive x-axis if the work done by the force in moving a particle from (0,0) to (4,0) equals 2.

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…

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

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Q: In what direction from the point (1,-1) is the instantaneous rate of change of f(x.y) = 8x* – 10x?y?…

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Q: Find the velocity and acceleration vectors of the particle whose position at time t seconds is given…

A: We have a given position vector of any particle. And we have to find velocity and acceleration…

Q: Find the tangential and normal components of acceleration for a projectile fired at an angle 0 with…

A: we know that for projectile fired at angle θ with the horizontal tangentialTt and normalNt…

Q: Determine the flow rate of water across the net if the velocity vector field for the river is given…

A: The given velocity vector field is,V=<x-y, z+y+4, z2>The net is given as:x2+z2≤1 and y=0Assume…

Q: Find the work done in pushing a car a distance of 12 m while exerting a constant force of 300 N.

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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: 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: Find the velocity and acceleration vectors in terms of u, and ug. r= 6 sin 2t and 0 = 4t v=u, +Due…

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Q: Find a unit vector in the direction in which f (x, y) = 8 cos(5x – 3y) decreases most rapidly at P…

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Q: Find the velocity and acceleration vectors in terms of u, and ug- r= a(4+ sin t) and 0 =9- e -t,…

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Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a sin 30 and =7t, where a is…

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Q: Express the velocity and the acceleration of a moving point p(r,0)

A: We have given a curve in polar coordinate : r=1+sin(θ) with θ=t2…

Q: Find the directional derivative of f at P in the direction of a vector making the counterclockwise…

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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 velocity and acceleration vectors, and speed for r(t) = (sin(3t), cos(t), cos(: OS…

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Q: Suppose only F acts on the object and with this force only, the object experiences a displacement…

A: Introduction: When a force is acted upon an object, there is a displacement. The dot product of the…

Q: Find the work done by the force F = 3i − 9j in moving an object from the point (3, 3) to the point…

A: To find work done.

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

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Q: A particle's position vector is given by: F(t) = R(1+ cos(wot + q cos wot))& + R sin(wnt + q cos…

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Q: Find a unit vector parallel to the tangent line of y = x at (2,8). What angle does this vector make…

A: Given that, y=x3   We have to find a unit vector parallel to the tangent line of the given curve at…

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

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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: Here it is given that a force of 200N is applied at an angle of 30 degrees from horizontal to move a…

Q: Find the work done (in Joules) in pushing a car a distance of 8 meters while exerting a constant…

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Q: Q6/ A boxful has been moved a distance (2m) in a F = 5.2 i+ 3J horizontal direction due to effect of…

A: Work done by a force is equal to the product of Force applied in the direction of distance and…

Q: Calculate the velocity and acceleration vectors, and speed for r(t) = (sin(t), cos(3t), cos(t)) when…

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Q: What would be the resultant force F of the triangular distributed load and its location 'd' measured…

A: Given,

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

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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…

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

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Q: For time 1 > 0, the position of a particle moving in the xy-plane is given by the parametric…

A: Velocity==rate of change of distance per unit time=displacementtime=dsdt. Given that: x=4t+t2  and…

Q: Find the work W done by a force of 77 pounds acting in the direction 30° to the horizontal in moving…

A: We will use the formula:

Q: A lawn mower has a mass of 30 kg. It is being pushed with a force of 100 N. If the handle of the…

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Q: If a particle travels with constant speed, must its acceleration vector be zero? Explain

A: Given- If a particle travels with constant speed, must its acceleration vector be zero? To Explain-…

Q: Find the velocity and acceleration vectors in terms of u, and ug- r=5 sint and 0= 5t = (5 cost) u, +…

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Q: It takes 1700 J of work to stretch a spring from its natural length of 1 m to a length of 6 m. Find…

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Q: Find the work required to compress a spring from its natural length of 1 ft to a length of 0.75 ft…

A:

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

A:

Q: Find the work done by the force F = 7i − 9j in moving an object from the point  (8, 8)  to the…

A: Work done= Force X Displacement

Q: Find the work done by the force F= 6i – 2j in moving an object from the point (1, 7) to the point…

A: Work done by force F→ in moving object from point P to point Q is given by F→.PQ→ , where PQ→ = OQ→…

Q: A ball is bounced directly south, with an initial velocity of 10 m/s off the ground, with an angle…

A: Given initial velocity of ball is 10 m/sec. Angle of elevation is 30°. The ball moves at a constant…

Q: Write Newton’s Second Law of Motion for three-dimensionalmotion with only the gravitational force…

A: It is known that, by Newton's second Law of motion the value of force is, F=ma. Or equivalently,…

Q: Find the angle of tilt θ with the horizontal so that the contact force at B will be equal to 0.76…

A: Draw the free body diagram of the block.

Q: A force of 6 newtons is applied in the direction of the vector v = 2i + 2j - k. Express the force F…

A: Given vector, v=2i+2j-k

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…

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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: The minute hand of a wall clock measures 24 cm from its tip to the axis about which it rotates. The…

A: Given: The minute hand of a wall clock measures 24 cm from its tip to the axis about which it…