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What should be the spring constant $k$ of a spring designed to bring a 1300 -kg car to rest from a speed of 90$\mathrm { km } / \mathrm { h }$ so that the occupants undergo a maximum acceleration of 5.0$\mathrm { g }$ ?

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$5.0 \times 10^{3} \mathrm{N} / \mathrm{m}$

Physics 101 Mechanics

Chapter 7

Work and Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

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04:05

In physics, a conservative force is a force that is path-independent, meaning that the total work done along any path in the field is the same. In other words, the work is independent of the path taken. The only force considered in classical physics to be conservative is gravitation.

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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.

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What should be the spring …

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(II) What should be the sp…

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II) What should be the spr…

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A $1200-\mathrm{kg}$ car …

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(II) A 1200-kg car moving …

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(II) A $1200 - \mathrm { k…

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(II) A 1200 -kg car rollin…

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A car's 30.0 -kg fron…

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A 950 -kg car strikes a hu…

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A $5.00 \times 10^{5}$ -kg…

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here, we need to find the spring constant. So we know that the work of the spring is going to be equal to the change in kinetic energy. And this will be able to 1/2 times, um, the final squared minus fi initial squared. And we know that this this is coming to a stop. So the final philosophy will be zero on. We can say that the work done by the spring is 1/2 k x squared and this is equaling negative 1/2 and the initial squared. So essentially, we know that X is going to be equal to the initial times the square root of the mass divided by the spring constant. And we know that forces equaling the mass times acceleration, which will equal negative K x. Ah, And here we can say that mass times negative 5.0 G is going to be equal to negative kay times the initial times the square root of over K. So here we're substituting negative five times the acceleration due to gravity for the acceleration. And then for X here were substituting this equation here on DH. Then, at that point, we can solve for K and K is going to equal mm times five g, divided by the initial quantity squared and we can solve. So let's get any work book actually and said that Kay is going to be equal to 1300 kilograms times 25 times 9.8 meters per second squared, all divided by 90 kilometers per hour. Most fly by 1000 meters per kilometer and then there for every one hour. There are 3600 seconds and then we're gonna have to square this entire term. So we find after evaluating the spring, constant is going to be equal to 5.0 times 10 to the third Newtons per meter. And so this would be our final answer. That is the end of the solution. Thank you for watching.

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