A simple spring is used to measure force. The spring isconsidered to be linear, so that F = kx, where F is the force inNewtons, k is the spring constant in newtons per centimeter,and x is the displacement in cm. If x = 12.5 + 1.25 cm and k =700 + 18 N/cm, calculate the best estimate of the uncertaintyof the measured force in relative terms (i.e., in terms of % ofthe measured force).

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Answered: A simple spring is used to measure…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Suppose that the vertical position axis x is oriented upward A shell of mass 2 kg is shot upward with an initial velocity of 100 m/sec. The magnitude of the force due to air resistance is with x = 0 at ground level. Denote by x(t) and v(t) the position and velocity of the shell at time t (in seconds). The acceleration due to gravity has magnitude g=9.81 m/sec². 20 The following numerical values might be useful in the calculations: In 1.96= 0.764, In 98.04 =4.58, In 392.4 = 5.97, In 492.4 = 6.20 (a) Find the differential equation satisfied by v(t) O A. dv V + dt 40 = -9.81
A force of 175 newtons stretches a spring by 5 meters. What is the value of the constant of proportionality (the spring constant)? Round your answer to the nearest hundredth, if necessary.
It takes a force of 21,882 lb to compress a coil spring assembly from its free height of 6 inches to its fully compressed height of 3 inches. a. What is the assembly's force constant? b. How much work does it take to compress the assembly the first half inch? the second half inch? Answer to the nearest in-lb. a. k= lb/in
A man and his parachute weigh 160 lbs and fall from rest to the ground. Before he parachute opens, air resistance (in pounds) is numerically equal to 1/2v (where v is the instantaneous velocity in ft/s) and, from the moment it opens, the resistance is 5/8 v2. If the parachute opens at 5 s, calculate the skydiver's velocity at any second t: a) Before opening the parachute. b) Find the distance he has fallen before the parachute opens. c) After opening the parachute. topic: ORDINARY DIFFERENTIAL EQUATIONS
Use the method of Variation of Parameters to solve the following DE: у" — у %3D 2х2 —х — 3. 3.
A researcher is nuning a simulation of an upward rocket to study the upward velocity of the rocket using various fuel consumption rates. The researcher has found that the upward velocity of the rocket can be represented by the following equation, mo v = u In gt Amo-qt. where v=upward velocity of the rocket (m/s), u= the velocity at which fuel is expelled relative to the rocket (m/s), m, = the initial mass of the rocket (kg), q = the fuel consumption rate (kg/s), g = the downward accelemation of gravity (m/s), and t = time taken by the rocket for the whole motion (s). If u = 1,500 m/s, m, = 125,000 kg, q = 2,300 kg/s and g= 9.81 m/s are the values used by the researcher in one of his simulations, estimate the time, t at which v = 680 m/s using False Position method. It is known that the time, t is somewhere between 15 s and 35 s. Perform THREE (3) iterations only and calculate the approximate percent relative error, Ea| for every iteration.

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