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$\bullet$ $\bullet$ Four passengers with a combined mass of 250 $\mathrm{kg}$ compress the springs of a car with wom-out shock absorbers by 4.00 $\mathrm{cm}$ when they enter it. Model the car and passengers as a single body on a single ideal spring. If the loaded car has a period of vibration of $1.08 \mathrm{s},$ what is the period of vibration of the empty car?

1.003$\mathrm{s}$

Physics 101 Mechanics

Chapter 11

Elasticity and Periodic Motion

Equilibrium and Elasticity

Periodic Motion

Cornell University

University of Washington

McMaster University

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

02:18

In physics, an oscillation is the repetitive variation, typically in time, of some measure about a central value or between two or more different states. The oscillation may be periodic or aperiodic.

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eso for this question. It was asking us what is the period of vibration off the empty car? Well, we know the period is equal to one over frequency. We just went over and the for consider, right? You have to buy and give us two powerful omega, which is the angular frequency. And Omega is equal to the square root K o m. Which is the force Constant doing biomass. And we caught him back to the T question Will get through pi over square. Okay, over m, which will give us t 0 to 2 pi times. It's where, um okay, okay. And we know the force Constant K is equal to force to Dubai by the displacement. Okay, so Well, let's figure out, OK. First name for his case. It's okay to go. The force and force that is involving is the question. Is the gravity off the four passenger somebody? So is mg Okay? You have my axe. Remember that massive A four passenger was 250 kilograms. The gravitational constant is 9.8 year for seconds where any compressed four centimeter, according to the question So which is 0.4 meter and this will give us 61 250. I knew Tom a meter. Okay, so the force constant is Ah, 61,000 and 250. Your car per meter. So now we know that initial period was given as one point. Oh, a seconds. An initial period is equal to to buy Times Square root the massive passenger plus the mass of a car. Okay, over the force. Constant and ah, time here for the empty car is equal to pi. It has screw off the massive car over force. Constant. Huh? So now we have the forest constant. So in order to determine the time period for an empty car, we need to find out the mass off the car. Okay? And in order to figure out the massive a carpet and go back to the equation T i with two pi times square MP bus, EMC over K, because miss off the passenger skill, it was just 252. Okay? And we also know the force constant is 61,000. I'm sorry. 6000. 61,000 and one, 250. You know something meter and we know the time period for the car and a passenger. It is one point away sector. So this will give us MD car is just equal to t I. Which is the initial period over troop I square times, the force constant. And then my sister mass over the passenger. Okay, so this is from the this equation here. So this is to this, Okay? It was on simplification, and you'll get a question. I got down here. Good. So if we plug in a value, we'll get G I, which is 1.0, a second over to buy square times the force constant, which is just do you 1000 and 250. No tongue. Come here and minus the massive passenger was just 250 kill worms. And this will give us the mass of Emily Carr of. And the car is 2000 and 559 or in six two groups. Okay, No, for the period off the empty car is with the to buy times square room M car over the force constant. This will give us the periods just simply with the two pi Times Square. Oh, mescal. Car wishes 15 59. 26 kilograms over the force Constant, which is 61,000 and 250. Utah meter. Okay, this will give us the time. Here is about one point zero 0 to 6 seconds if we round up. So the third digits give us 1.3 second. Okay. And that's the answer. Forties question. Thank you.

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