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$\bullet$ Bumper guards. You are asked to design spring bumpersfor the walls of a parking garage. A freely rolling 1200 $\mathrm{kg}$ carmoving at 0.65 $\mathrm{m} / \mathrm{s}$ is to compress the spring no more than7.0 $\mathrm{cm}$ before stopping. (a) What should be the force constantof the spring, and what is the maximum amount of energy thatgets stored in it? (b) If the springs that are actually deliveredhave the proper force constant but can become compressed byonly $5.0 \mathrm{cm},$ what is the maximum speed of the given car forwhich they will provide adequate protection?

a) $1.03 \times 10^{5} \mathrm{N} / \mathrm{m}$b) 0.46 $\mathrm{m} / \mathrm{s}$

Physics 101 Mechanics

Chapter 7

Work and Energ

Physics Basics

Applying Newton's Laws

Kinetic Energy

Potential Energy

Energy Conservation

Cornell University

Simon Fraser University

McMaster University

Lectures

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problem Number 77. In this problem, it is given that I spring is to be designed, which will be used for Is stopping the rolling cars and given in formation is the moss off? The car is m equals well. One date 30 The velocity. Oh God! Issue quill 0.65 meter per second. The maximum compression off this spring should be X equals zero point 07 meters And we have to find that it's spring constant. That is gay quits. What for? First part. A par we can conclude. Hedda, can you take energy off? The rolling car should be absorbed completely by the spring. So that car it stops mine does No. Can it again? Ity at its final position. So the initial Canada tick energy have em. You square should be called to a spring potential energy that this half Okay, ex describe. This implies that well under intell zero point 65 square. Is it called a tow? Okay. In tow. Tzeitel. Why? 07 You square. This will go us the spring. Constant care as one born to 03 into 10 to the power five Newton. But I mean that Now we have to calculate the maximum and a G stored in the spring. The maximum energy this spring is equal to half. Okay, X is squad sequel toe half in tow. 1.3 into 10 to the power five into 0.7 you square which will give us 253 We're in five Jos. Now, for the second part of the question, we are given that for this force Constant which we opened in the five A. And for maximum compression excess school to 0.5 meters. What should be done? Velocity off the rolling car. Let this we lost Stevie. Then again, employing the concept off can take energy is a call to a spring energy does No, Um the square is We could do have Okay. Exes, Grad now associating the given real Use half in tow. Tell 100 into e square physical toe off into 1.3 into 10 to the power five in tow. Zero point 05 the square. This will give us the velocity off the rolling car as 0.4 three me dead. But second

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