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II) What should be the spring constant $k$ of a spring designedo bring a 1200 -kg car to rest from a speed of 95 $\mathrm{km} / \mathrm{h}$ sohat the occupants undergo a maximum acceleration of 5.0 $\mathrm{g}$ ?

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$4100 \mathrm{N} / \mathrm{m}$

Physics 101 Mechanics

Chapter 8

Conservation of Energy

Work

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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Rutgers, The State University of New Jersey

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Lectures

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.

04:30

In classical mechanics, impulse is the integral of a force, F, over the time interval, t, for which it acts. In the case of a constant force, the resulting change in momentum is equal to the force itself, and the impulse is the change in momentum divided by the time during which the force acts. Impulse applied to an object produces an equivalent force to that of the object's mass multiplied by its velocity. In an inertial reference frame, an object that has no net force on it will continue at a constant velocity forever. In classical mechanics, the change in an object's motion, due to a force applied, is called its acceleration. The SI unit of measure for impulse is the newton second.

02:45

(II) What should be the sp…

03:58

04:38

02:22

What should be the spring …

01:22

(II) A 1200-kg car moving …

02:04

(II) A $1200 - \mathrm { k…

01:29

(II) A 1200 -kg car rollin…

01:57

(II) A $1200-\mathrm{kg}$ …

02:19

A $1200-\mathrm{kg}$ car …

01:34

An object of mass $1 \math…

03:03

A 950 -kg car strikes a hu…

01:00

A $5.00 \times 10^{5}$ -kg…

04:03

A 2.0-kg object is attache…

02:20

A car of mass $1000 \mathr…

01:58

A car with a total mass of…

01:37

$\bullet$ An object of mas…

the first thing we're going to do is convert the lost the initial velocity from kilometers per hour, two meters for second, which we which we know how to work with. So kilometer one kilometer is 1000 meters, so that's 95,000 meters per hour. I want to convert that to meet us for seconds and we must find by one over 3600. So that's one hour for 3600 seconds. On this, you can see the hours cancel out. We get 26.38 meters per second. Is the initial velocity Okay, that's step one. Step two is using Newton's second law and so the net force is equal to mass times acceleration. So in this case, this case mass times acceleration will be cooled to the special force of the spring. So negative, K x and therefore X It is X is negative care. Whoops. Not negative care X is negative. I m f over kept. All right. So once you have that, you can move on to, um the next step, which is energy conservation, okay. And so that the use of WeII said we equate the initial kinetic energy which is 1/2 of me not squared to the elastic potential 1/2 k x square one has cancel. And now we'll place X with with with what we know it to be, which is negative a over care on dso That's k times of right hand side. You have k times negative am over Carrie Times, eh? Uh, squared. Okay, so moving on to the next page, we have em Venus squared. He calls to kay times. Uh, I'm squared over k squared. Time's a squared. Okay. And so one of these kids cancel one of these arms. Cancel What you get is view, not squared or let's recommence write things down in terms of K know his cares what we want. So what you get is care is equal to em a squared over Venus squared, remember, A is just fine. Maximum acceleration, which is five g. So m times five cheese squared over Venus squared. In other words, five square is 25. He squared s o. That's 25 m times. She squared over few, not square. And so we can plug in numbers. Okay, is 25 times mass which is 1200 kilogrammes times acceleration due to gravity, then pointed me disperse. Second squared quantity squared over Venus squared, which is 26.38 meters per second quantity squared, and this gives us 4100 Newtons per meter as the spring constant needed.

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