Write Newton’s Second Law of Motion for three-dimensionalmotion with only the gravitational force (acting in the z-direction).

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: Work of 2 Joules is done in stretching a spring from its natural length to 20 cmcm beyond its…

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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: Find the fluid force on the vertical plate submerged in seawater

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Q: When body is an equilibrium ,the net force is vanish

A: We have to check whether the given statement, "When body is an equilibrium, the net force is vanish"…

Q: onent. Determine the moment exerted about the steering column at O.

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Q: A 5500-pound vehicle is driven at a speed of 30 miles per hour on a circular interchange of radius…

A: As , f=mv2rGiven , m=5500 pound ,v=30 miles/hr , r=100 feetv=44 ft/s

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: A man on the edge of a platform 8 ft above the ground throws a ball vertically upwards with an…

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

Q: What is meant by a tangent vector?

A: To Explain:  a tangent vector

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

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Q: When body is an equilibrium ,the net force is not vanish

A: False. The given statement is false. We know that: There are two conditions that must be met for an…

Q: Consider a particle that moves around a circle. Is the velocity vector of the particle always…

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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: What is the length of the acceleration vector of a particle travelingaround a circle of radius 2 cm…

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Q: What is the derivative of a function ƒ(x, y) at a point P0 in the direction of a unit vector u? What…

A: For a function z=f(x,y): the partial derivative with respect to x gives the rate of change of f in…

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: Is the bicyclist's acceleration positive, negative or zero? Explain.

A: To determine whether the bicyclist's acceleration of positive, negative, or zero.

Q: 7. A 2600-pound truck is stopped at a red light on a hill with an incline of 25°. Ignoring the force…

A: Recall:  Force=w·sin θ We have, w=2600 pounds, θ=25°

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: A small cart is being pulled along a smooth horizontal floor with a 20-lb force F making a 45° angle…

A: The method of resolving force vectors into their x- and y-components is component of a vector.…

Q: Explain why you integrate in the vertical direction (parallel to the acceleration due to gravity)…

A: To Explain why do we integrate in the vertical direction (parallel to the acceleration due to…

Q: Q2. A point is moving along a curve whose position vector is Find : the acceleration components at /…

A: Consider the given position vector

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: if the velocity function vector v = 3t 1+ tJ- 2k find the acceleration( a). -

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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: When fluid force acts on the side of a submerged object, in which direction does it act?

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Q: If a force of 1.15 x 103N is required to lift an object with a uniform velocity, determine the mass,…

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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…

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Q: The automobile has a mass of 2 Mg and the center of mass at G. Determine the towing Q3 30 force F…

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

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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 body of mass n: moves along Y such that at time t its position is y(t) = at3/2 - bt + c, where a,…

A: a) Given the position of the body at a time t is given by yt=at32-bt+c where a,b,c are constants.…

Q: Find the resulting force, R what additional force F is needed for the object to be in static…

A: F1 = -12i + 8j F2 = -9i - 15j F3 = 11i + 7j Resulting force is the sum of all the forces. Static…

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…

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

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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: As part of a skydiving course, a diver jumps out of a plane 64 ft above the ground with an initial…

A: To find the velocity of the diver at the moment the diver lands on the ground.

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: Assume that a spring does not follow Hooke’s Law. Instead, the force required to stretch the spring…

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Q: Determine the moment of inertia about y-axis

A: This is a problem related moment of inertia of composite sections. Based on general formula and…

Q: Derive the equation of torsion and discuss its usefullness and limitations in detail ?

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Q: Determine where the resultant force acts measured from point O.

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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 ,

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.