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The coefficient of kinetic friction between a suitcase and the floor is 0.272 . If the suitcase has a mass of 71.5 $\mathrm{kg}$ , how far can it be pushed across the level floor with 642 $\mathrm{J}$ of work?

3.37 $\mathrm{m}$

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Rutgers, The State University of New Jersey

Numerade Educator

Hope College

University of Winnipeg

Okay, we have that. The coefficient of kinetic friction between a suitcase and the floor is 0.272 Okay, so Mu is equal to 0.272. All right? And this is between some suitcase, okay? And the floor. Okay, so here we've got some friction, and that's the go fishing there. Okay, if this suitcase has a mass of 71.5 kilograms, Okay, how far can it be pushed across the level floor with 642 jewels of work? Okay, so we have this much energy, we gotta push this suitcase. All right? So the first thing that we're gonna have to find out here is what the force of friction is gonna be. OK, so how we gonna find the force of friction to the force of friction? Okay. F little F right here is going to be new times. The normal force. Okay. The normal force is simply going to be okay. So we have mg coming down here and f n against it. So the normal force is gonna be the same magnitude is gravity. Okay, So normal forces just mg and the frictional force is mute Times mg. Okay, so we have the frictional force is gonna be mu M g. Okay. And we have to push this some distance, and ah, we apply this force over some distance that's gonna take energy that's doing work. Right? So we're gonna have mu m g X. Okay, that's the work. It's the equation for work here, So this is the same as f f. Multiply that by the distance. All right, this has to some 2 642 jewels. OK, that's how much energy were given. So we set it up like this. Mu M g X equals 642 all right? And what we're really interested here in here is X, so we solve for X. So X is going to be 6 42 divided by mu, which is 0.272 multiplied by M 71.5 and multiplied by G 9.8. Okay, let's do that calculation. So we got 6 42 divided by point 272 divided by 71.5 and divided by 9.8. Okay. And the answer is 3.37 meters. Okay, so this is gonna be 3.37 meters. Okay, So X equals 3.37 meters.