Assume without loss of generality that the parabola is described by , for A, B > 0, and that an object of mass m is situated initially at (x0 , y0 )= (0, A) at rest before being given a tiny nudge towards positive x.
a) Use energy methods to determine the speed of the particle as a function of x.
b) Calculate the radius of curvature r(x) for the parabola.
c) Given dy/dx = tan(), by definition, determine cos() in terms of dy/dx. (Draw an infinitesimal triangle.)
d) Use Newton II in the radial/normal direction to determine the magnitude of the normal force N(x) and show that it is always strictly positive for this problem.
use concepts of work and energy, trigonometry
Assume without loss of generality that the parabola is described by , for A, B >...
2 parts, thx:) 1) Current of 4.0 A flows in the coil as shown in the figure. The coil has 4 loops and is situated in the xz-plane. The area of the coil is 3.00 x 10-3 m2. The coil is situated in a uniform magnetic field = (2.00- 5.00- 5.00mT. What is the magnitude of the torque acting on the loop due to the magnetic field? Give your answer in µNm (micro-Newton meters). 2) Current of 2.0 A flows...
Find the solution to the given systems (a) X'=X X(0)= (b) dx/dt=5x+y dy/dt=-2x+3y We were unable to transcribe this imageWe were unable to transcribe this image
Consider the boundary value problem for the general second-order equation with constant coefficients y(a)=YA, y(b)=YB Let the interval a<x<b divided into n subintervals of width h=(b-a)/n.Using central difference approximations find the lineer system that must be solved to approximate y2,y3,,,yn We were unable to transcribe this image01.2 h2 2h We were unable to transcribe this imageProblem 3 boundary value problem for the general second-order equation with constant coefficients dy dy y(a) YA, ybYB. Let the interval a s b be...
Suppose you are riding a bike on the plane without slipping. The latter condition of ”no slipping” means that if is a point in the trajectory of the back wheel of the bicycle, then the front wheel lies on the tangent line to at point p: In this problem you will be proving, step-by-step, the following theorem: Bike theorem: If a bike with a frame of length b made a loop on the plane without slipping, so that the traces...
We were unable to transcribe this imageB. Analyze the torques acting on the beam while in equilibrium with the pivot point indicated and determine the normal force provided by triangle support A. Clearly show your reasoning and work. Consider CW as positive. (6 pts) het forue t tbrque fn 8.3 1.2110)(EL)-10D 12(00 12 12 fL-8.3 B. Analyze the torques acting on the beam while in equilibrium with the pivot point indicated and determine the normal force provided by triangle support...
Learning Goal: To be able to identify the initial stresses and the angle of rotation, including the correct signs, and use these in the stress-transformation equations to find the stress on a plane or element at a different angle than the original. The method of calculating the state of stress on an inclined plane is tedious, prone to error, and incomplete—if we calculate σx′ and τx′y′, we have to do a separate calculation to determine σy′. Consider the stress element...
Hi need help for these Questions: a. Given f = yi + xzk and g = xyz2, determine (∇ x f ) . ∇g at the point (1,0,3) b. Point A lies on the curve r(t) = 2 cos t i + 2 sin t j + t k for the range 0 ≤ t ≤ 2π . At point A, the tangent vector is T = - 21/2i + 21/2j + k. Determine the co-ordinates of point A and...
The cylinder consists of spirally wrapped steel plates that are welded at the seams in the orientation shown. Assume β = 20°. The cylinder has an inside diameter of 34 in. and a wall thickness of 0.3750 in. The end of the cylinder is capped by a rigid end plate. The cylinder is subjected to a compressive load of P = 125 kips and a torque of T= 210 kip-ft, which are applied to the rigid end cap in the...
plz can you help me with this I only need the answer. only the answers please I will rate you yes 18:32 Thu 9 May 75 %- sin(x) dy = 0.9461 (2n+1) (2n1)! Need Help?Read lit Talk to a Tutor 12. 0.34/1 points | Previous Answers LarCalc11 9.10.073. My Notes Ask Your Approximate the normal probability with an error of less than 0.0001, where the probability is given by the following. (Round your answer to four decimal places.) x2/2 dx...
sics for Scientists and Engineers 4th ed (1.pdi-Adobe Acrolst Reader Dc Window Help ools Giancoli Physics fo... x 93 1322 111% EXAMPLE 21-11 Long line of charge. Determine the magnitude of the electric field at any point P a distance x from the midpoint 0 of a very long line (a wire, say) of uniformly distributed positive charge, Fig. 21-29. Assume x is much smaller than the length of the wire, and let λ be the charge per unit length...