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Suppose you are an engineer for a motorcycle manufacturer. You are assigned to the team designing the motorcycle's rear suspension. You are studying the properties of springs that are strained horizontally. Your experimental setup is animated in the simulation (linked below). In this simulation, a particle is given an initial velocity at x = 0, and it moves in the + x direction while slowing down due to the elastic force. When the block is at x = 0, the spring is unstrained, and therefore exerts no force on the block. So x = 0 is the particle's equilibrium location. The end of the interval is taken to be at the one-meter mark, which is where the particle is momentarily at rest. That is, x₂ = 1 m. Run the animation now. Simulation The Elastic Force Acts on a Moving Block The simulation shows the true spring force on the block as it moves (see the solid blue arrow labeled "Exact Force"), and it also shows an approximation to the exact force (see the dashed blue arrow labeled "Approximate Force"). Note the behavior of the approximate force. It jumps discontinuously to a new value each time the block completes a displacement of size Ax = x₂/N. Both the true and the approximate forces are plotted in the simulation above the animated motion. The area between the plot of the approximate force and the x-axis is a series of narrow rectangles shaded in light blue in the simulation. The exact force is the line Fx = kx, which is shown in green in the plot.

Suppose you are an engineer for a motorcycle manufacturer. You are assigned to the team designing the motorcycle's rear suspension. You are studying the properties of springs that are strained horizontally. Your experimental setup is animated in the simulation (linked below). In this simulation, a particle is given an initial velocity at x = 0, and it moves in the + x direction while slowing down due to the elastic force. When the block is at x = 0, the spring is unstrained, and therefore exerts no force on the block. So x = 0 is the particle's equilibrium location. The end of the interval is taken to be at the one-meter mark, which is where the particle is momentarily at rest. That is, x₂ = 1 m. Run the animation now. Simulation The Elastic Force Acts on a Moving Block The simulation shows the true spring force on the block as it moves (see the solid blue arrow labeled "Exact Force"), and it also shows an approximation to the exact force (see the dashed blue arrow labeled "Approximate Force"). Note the behavior of the approximate force. It jumps discontinuously to a new value each time the block completes a displacement of size Ax = x₂/N. Both the true and the approximate forces are plotted in the simulation above the animated motion. The area between the plot of the approximate force and the x-axis is a series of narrow rectangles shaded in light blue in the simulation. The exact force is the line Fx = kx, which is shown in green in the plot.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Using the geometrical approach based on areas just described in question 1, you can find the total work done by the approximate force over the displacement between x = 0 and x = x2. What is this approximate work for the case of N = 4?

Suppose you are an engineer for a motorcycle manufacturer. You are assigned to the team designing the motorcycle's rear suspension. You are studying the properties of springs that are strained horizontally. Your experimental setup is animated in the simulation (linked below). In this simulation, a particle is given an initial velocity at x = 0, and it moves in the + x direction while slowing down due to the elastic force. When the block is at x = 0, the spring is unstrained, and therefore exerts no force on the block. So x = 0 is the particle's equilibrium location. The end of the interval is taken to be at the one-meter mark, which is where the particle is momentarily at rest. That is, x₂ = 1 m. Run the animation now. Simulation The Elastic Force Acts on a Moving Block The simulation shows the true spring force on the block as it moves (see the solid blue arrow labeled "Exact Force"), and it also shows an approximation to the exact force (see the dashed blue arrow labeled "Approximate Force"). Note the behavior of the approximate force. It jumps discontinuously to a new value each time the block completes a displacement of size Ax = x₂/N. Both the true and the approximate forces are plotted in the simulation above the animated motion. The area between the plot of the approximate force and the x-axis is a series of narrow rectangles shaded in light blue in the simulation. The exact force is the line Fx = = kx, which is shown in green in the plot.
Transcribed Image Text:Suppose you are an engineer for a motorcycle manufacturer. You are assigned to the team designing the motorcycle's rear suspension. You are studying the properties of springs that are strained horizontally. Your experimental setup is animated in the simulation (linked below). In this simulation, a particle is given an initial velocity at x = 0, and it moves in the + x direction while slowing down due to the elastic force. When the block is at x = 0, the spring is unstrained, and therefore exerts no force on the block. So x = 0 is the particle's equilibrium location. The end of the interval is taken to be at the one-meter mark, which is where the particle is momentarily at rest. That is, x₂ = 1 m. Run the animation now. Simulation The Elastic Force Acts on a Moving Block The simulation shows the true spring force on the block as it moves (see the solid blue arrow labeled "Exact Force"), and it also shows an approximation to the exact force (see the dashed blue arrow labeled "Approximate Force"). Note the behavior of the approximate force. It jumps discontinuously to a new value each time the block completes a displacement of size Ax = x₂/N. Both the true and the approximate forces are plotted in the simulation above the animated motion. The area between the plot of the approximate force and the x-axis is a series of narrow rectangles shaded in light blue in the simulation. The exact force is the line Fx = = kx, which is shown in green in the plot.
Number of intervals, N Felastic (N) 0.0 -0.5 -1.0 -1.5 -2.0 www. 02 x₁ = 0 0.4 0.6 0.8 x (m) 1.0 C=0.000 = 4.000
Transcribed Image Text:Number of intervals, N Felastic (N) 0.0 -0.5 -1.0 -1.5 -2.0 www. 02 x₁ = 0 0.4 0.6 0.8 x (m) 1.0 C=0.000 = 4.000
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