The velocity v (m/s) of air flowing past a flat surface is measured at several distances y(m) away from the surface. Use Newton's viscosity law to determine the shear stress t (N/m2) at the surface (y=0). dv To dy Assume a value of dynamic viscosity u=1.8. 10-N.s/m2 0 0.002 0.006 0.012 0.018 0.024 0 0.287 0.899 1.915 3.048 4.299 y, m V, m/s (=?) Apply Richardson extrapolation. Estimate the approximate percent relative error

Q: The pressure of a fluid flowing through a closed system, P, after t seconds can be modeled by the…

A:

Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)2(1 + 8.8)3 −…

A:

Q: z = e*sin y, Mo (1,2) 6

A:

Q: A retarding force, symbolized by the dashpot in the figure to the right, slows the motion of the…

A:

Q: Estimate ∆ y using differentials equ ∆y ≈ dy = f ' (a)dx y = cosx, a= π/6, dx = 0.014

A: Given y = cos x  a= π/6, dx = 0.014

Q: Assume that after few w months, butterf lies papulace in looa is Calculated as: F(w)=12W+Cos (lbw)…

A: Minimum and maximum of a function can be calculated by testing the function against all the values…

Q: Compute the work required to stretch a spring from 7 to 14 cm past equilibrium, assuming that the…

A:

Q: A particle moves around the unit circle in the xy-plane. Its position at time t is r = xi + yj,…

A: Given information:

Q: A ball having mass m falls from a tower with heigh h from the ground. The velocity of the ball…

A: A differential equation in the variable separable form can be evaluated by shifting all terms of one…

Q: A uniform sphere of mass m rolls from rest at A along a frictionless hemispherical surface, under…

A: Consider the given figure as

Q: Given a particle is moving in a curve r(t) = cos  6t i + sin 6t j +  10t k. Find the tangential…

A: I have appended the formula used in the solution part

Q: From a height of 7 meters above ground level, a rock with mass m = 4 kg is hurled into the air with…

A:

Q: A particle has velocity v(t) = 3t² – 2t – 1, measured in meters per second. Compute the displacement…

A: A  particle has velocity  vt=3t2-2t-1, measuredin meters per second, compute  the displacement  of…

Q: Given a particle is moving in a curve r(t) = cos 8t i + sin 8t j+ 8t k. Find the tangential…

A: The given curve is r(t)=cos 8t i + sin 8t j + 8t k

Q: Given a particle is moving in a curve r(t) = cos 8t i + sin 8t j+ 5t k. Find the normal component of…

A:

Q: 9. Assume that an object moves with velocity v(t) = sin(t)+ ;. (a) Determine the displacement of the…

A: we have given velocity v(t)=sint+12(a) displacement  =∫02π(sint+12)dt…

Q: The surface area of a sphere is expanding at the rate of 6 cm²/sec, Wher What is the change in the…

A:

Q: A 5 kg weight is attached to a spring with constant k = 80 N/m and subjected to an external force…

A: Consider my¨+ky=Ft......1 Given that m=5 kg, k=80 Nm and Ft=140sin3t..…

Q: Compute the work required to stretch a spring from 4 to 15 cm past equilibrium, assuming that the…

A:

Q: Sketch a graphic representation and, using the differential length, calculate the length of the…

A:

Q: From a height of 7 meters above ground level, a rock with mass m = 4 kg is hurled into the air with…

A: NOTE: Refresh your page if you can't see any equations. . ..............(1) here we  have .

Q: Find the total differential. w = eбy cos(4x) + z7 dw (No Response)

A: Explanation of the answer is as follows

Q: A 20-lb weight is hung on an 18-in. spring stretching it 6 in. The weight is pulled down 5 in. and 5…

A:

Q: Compute the work required to stretch a spring from 7 to 13 cm past equilibrium, assuming that the…

A: Given query is to find the the work required.

Q: Given a particle is moving in a curve r(t) = cos 2t i + sin 2tj+ 4t k. Find the normal component of…

A:

Q: 4. A T meter long chain hangs from the top of a tall building as shown. If the linear density of the…

A:

Q: A 3 kg mass is attached to a spring with stiffness k = 48N / m. The mass moves 1/2 m to the left of…

A: The equation can be given as; y" + (k/m)y =0,   The mass moves 1/2 m to the left of the equilibrium…

Q: A unit mass hangs in equilibrium from a spring with constant k = 1/16. Starting at t = 0, a force F…

A:

Q: It takes 1,600 joules (J) of work to stretch a spring from its natural length of 4 meters (m) beyond…

A: W=12kA2, where A is stretched or compressed length of spring

Q: Find the total differential dw. 4. w = e*" – sin(yz) -

A:

Q: The radius of a spherical balloon is measured as 4 inches, with a possible error of 0.01 inch. Use…

A: The volume of the spherical balloon is measured as V=43πr3 a)Differentiate V=43πr3 with respect to r…

Q: 4 V ==T³, 3 where r is the radius, in centimeters. Compute the average rate of change of V with…

A: we have to find rate of change of volume with respect to r.

Q: Let y(t) be the position function of a particle in rectlinear motion. Suppose at time t = 0 hr, that…

A:

Q: Suppose that a particle moves along a straight line with acceleration defined by a(t) = t – 5/2 in…

A:

Q: It takes 50J of work to stretch a spring 0.2m from its equilibrium position. How much work is needed…

A:

Q: Compute the work required to stretch a spring from equilibrium to 8 cm past equilibrium, assuming…

A:

Q: f 5 J of work are needed to stretch a spring 10 cm beyond equilibrium, how much work is required to…

A:

Q: Find the total distance traveled by a particle according to the velocity function v(t) = 4t – 4…

A:

Q: A spring is stretched 6 in. when a 4-lb weight is hung on it. The 4-lb weight is attached and pushed…

A: When a mass is subtended from a spring, the string is stretched. The weight of an object is the…

Q: Find z = f(x, y) and use the total differential to approximate the quantity. (2.04)^2(1 + 8.8)^3 −…

A:

Q: A wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the…

A:

Q: Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a…

A:

Q: Find z = f(x, y) and use the total differential to approximate the quantity. (1.96)2(8.98) 2² (9)

A:

Q: (b) Calculate the rate of change of the function f(r, y, 2) = ryz along the path r(t) = (sin(t), e“…

A:

Q: The velocity v of a falling parachutist is given by v- gm/c (1 - o^-(c/m)t) where g- 9.8 m/s^2. For…

A: “Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: The volume V of a right circular cylinder of radius r and height h is V=πr2h (a) How is dV/dt…

A:

Q: Find the displacement of an object over the time interval, [0, t/4], given the velocity function,…

A: Here, the velocity function is given and we are required to find the displacement in the given time…

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.