=There is a compressed spring between two laboratory carts of masses m₁ 115 g and m₂ = 272 g. Initially, the carts are held at rest on a horizontal track as shown in figure A. The carts arereleased, and the cart of mass m₁ has velocity V₁ = 1.9351 m/s in the positive x direction as in figure B. Assume rolling friction is negligible.A.m₂V2√₂ = ?60000000m₁V₁B.(a) What is the net external force on the two-cart system? (Express your answer in vector form.)N(b) Find the velocity of cart 2. (Express your answer in vector form.)m/s

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Answered: There is a compressed spring between…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Consider r(t) = (cos(3t), sin(3t), 4t), the curve from #2. Find the principal unit normal vector to this curve at t = equation to the line normal to this curve at t = 플. 2. Write a vector
4). show all steps
show complete solution (computation and final answer must be in 4 decimal places)
13-41. A 150-mm-diameter shaft with a mass of 20 kg is rotating at 900 rpm. A pulley mounted on the shaft has a mass moment of inertia of 0.15 kg - m2. If the shaft and the pulley coast to a stop due to a tangential frictional force of 8 lb at the outer radius of the shaft, determine the time required.
A 360-kilogram go-cart is driven at a speed of 60 kilometers per hour around a circular racetrack of radius 12 meters, as shown in Figure . To keep the cart from skidding off course, what frictional force must the track surface exert on the tires?
3. Consider two charges of Q = 2x10 C at M(2, 1, 3) and a charge of Q2 =-3x10 °C at N(3, 0, 5) in a vacuum. Find the force exerted on Q2 by Qi.
A catenary cable is one which is hung between two points not in the same vertical line. As depicted in figure(right) it is subject to no loads other than its own weight. Thus, its weight acts as a uniform load per unit length along the cable w (N/m). A free-body diagram of a section AB is depicted in Fig. P6.17b, where TA and Tâ are ... the tension forces at the end. Based on horizontal and verti- cal force balances, the following differential equation model of the cable can be derived: W= ws (a) (b) 2 d²y dx² (dy` 1+ dx w %3D Calculus can be employed to solve this equation for the height of the cable y as a function of distance x: w TA y = cosh х) + yo — w w (a) Use a numerical method to calculate a value for the parameter TA given values for the parameters w = 10 and yo = 5, such that the cable has a height of y = 15 at X=200 The value of Ta is Blank 1. Express your answer in decimal with two decimal digits after the decimal point.
9. A vertical tower AO of height h metres stands with its base A on horizontal ground. A stone is projected horizontally from the top O of the tower with speed V ms ¹. The stone moves in a vertical plane under gravity where the acceleration due to gravity is g ms 2. At time t seconds its position vector relative to O is r(t) = Vt i-lgt² j The stone hits the ground at an angle of 45° to the horizontal. What is the time of impact? (A) (B) (C) (D) V 2g V g 2V g 4V g seconds seconds seconds seconds
(a) A pivot is placed under the beam at x = 4. Calculate the total torque around the pivot and state whether the beam is rotating clockwise or counter-clockwise. (b) The pivot is moved such that the beam is now in equilibrium. Find the new x-position of the pivot.
In the figure particle 1 of charge +5e is above a floor by distance d1= 4.60 mm and particle 2 of charge +8e is on the floor, at distance d2 = 6.00 mm horizontally from particle 1. What is the x component of the electrostatic force on particle 2 due to particle 1? di

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