Since it is known that the pouring time (T) of the sand in an hourglass depends on the height of the sand before it is poured (H), the density of the sand (ρ), the hole diameter (d) and the gravitational acceleration (g), obtain the phenomenon with the Buckingham pi theorem.

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

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Q: The force exerted by our home planet is GMx if x R, measured on a unit mass at a distance x from the…

A: We are given the function h(x) as the following. Notice that GMxR3 is continuous everywhere. And…

Q: An object has a weight of 60 N at a point where the acceleration due to gravity is g 10 m/s². What…

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Q: the wt starts from nest 2 ft' below tue E position and the subseguent tahos place in a weedium fuat…

A: Given mass = 16lb= 0.5kg damping constant ,k =16/(8/3)= 6 lb/ft f(t) =10cos3t β=  1/2= 0.5 The…

Q: function u (t) == C, cos(@ot – ao) that would result if the mass on the spring were set in motion…

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Q: When a certain spring is expanded 9 centimeters from its natural position and held fixed, the force…

A: Given query is to find the the work required to stretch the spring additional 9 cm

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: 2. When object P, with mass m, , moves at v, and object Q, with mass m,, moves at v,, the velocity…

A: Given,For P, mass = m1  and velocity = v1Let, velocity after collision is u1For Q,mass = m2 and…

Q: 1. Write the tangential and normal components of acceleration for = (tsint)i + (tcost)j + tk, at t-0

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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: Wer: 1088/3) 3. Compute the moment of inertia of the plate of constant density p described by -a <r…

A: Here is the moment of inertia of the plate of constant density ρ described by -a≤x≤a and -b≤y≤b…

Q: Given: R(t) = (cos t +tsin t) i + (sin t –t cos t) j + t?k^ ,t>0 What is the acceleration at t = EIN

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

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Q: Find the tangential and normal components of the acceleration vector. r(t) = cos(t)i + sin(t)j + tk…

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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: The following equation can be used to model the deflection of a sailboat mast subject to a wind…

A: As per the question we have the following second order nonlinear differential equation : y'' =…

Q: Find the unit tangent vector at t= 0: r(1) =tî+r° j+t°k

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Q: T 2 If fo)= J* +?dt, use the fundemental theorem of culculus part 1, to find f'cx) fixs=

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Q: 2. Given r(t) = et cos t i + e' sin tj + e'k , find the tangential and normal components of…

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Q: Complete the following definition: If r(t) =⟨x(t), y(t), z(t)⟩ is a twice-differentiable position…

A: Let y be the distance, so velocity is one time differentiation of distance with respect to time.…

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: Find the velocity and acceleration vectors in terms of u, and ug- do r= a(7 - sin 0) and =7, where a…

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Q: 2. Given r(t) = e' cos t i + e' sin t j+ e*k , find the tangential and normal components of…

A: Tangential component , aT = v.av  and Normal component , aN = a2-aT2

Q: Find the tangential and normal components of acceleration at the given time t for the plane curve…

A: The given plane curve is rt=ti+5tj, t=2.

Q: Consider

A: We find the general solution by finding roots of equation.

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: What force is required so that a particle of mass m has the position function r(t) = ti + 3t²j +°k?…

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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: Find the unit tangent vector (t) at the point with the given value of the parameter.. r(t) = (4te,…

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Q: Suppose it takes a force of 21 N to hold a spring that has been stretched from its natural length of…

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

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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…

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

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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: A projectile with mass m is launched into the air on a parabolic trajectory. For t >0, its…

A: In the absence of drag or viscous force , the total Mechanical energy of projectile remain constant

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

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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 while subjected to a…

A: Using formula for work done

Q: The force exerted by our home planet is GMx if x < R, R3 h(x) = GM if x 2 R, measured on a unit mass…

A: In the question we have to identify if the function is continuous.

Q: Compute the tangential and normal components and express the acceleration a in the form a= arT+aŋN…

A: Calculate the value for aT using the derivative.…

Q: Find the velocity and acceleration vectors in terms of u, and ug. de r= a cos 30 and = 4t, where a…

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Q: Suppose that r is the position vector of a particle moving along a plane curve and dA / dt is the…

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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.