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Problem 748, we're designing a delivery ramp for crates, and we have a 1470 newton crate that's moving at 1 .8 meters per second at the top of the ramp, and it goes down the ramp at a certain angle, and ramp exerts a friction force on each crate, and we have a maximum static friction force that is equal to that friction, kinetic friction value.
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So each crate will compress the spring at the bottom ramp, and it'll come to a rest after traveling five.
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Meters total.
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Okay, so and then one stop the create must not be bound up the ramp and we're supposed to find out the force constant is.
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So first off, i'm going to start off with just writing down the conservation of energy formula.
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So we have initially kinetic energy the create is moving, plus the gravitational potential energy.
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So then i'm going to write one g, u and then we're going to have work to do the friction.
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So plus work due the friction and at the end it's going to stop moving and we're saying that's at a potential of zero at the bottom of that five meters and then it's just going to have a elastic potential energy that is stored in the spring that was used to slow it down okay so let's find what each of those pieces are so k1 that's going to be straight forward we have that equal to 1 1 half times the mass.
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We don't have the mass.
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We have the force to gravity though.
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So we can just do 1470 divided by g and then times of all c squared 1 .8.
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So i'm not putting units on it right now, but you should know what those are.
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U1.
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Let's see.
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So we have this diagram over here.
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And if we break that into the components, what we can do is actually we don't to do that.
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You can just take the sign of 22 of this five meter length and then we get 1470.
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That's the gravitational force times five meters times sine of 22 degrees.
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Okay, so that should be our potential energy.
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Okay, now work due to friction.
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We're told explicitly what the force is.
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So that's 5 .15 newtons.
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We're told what the distance is.
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That's times 5.
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And we have to make sure we get the sign correct.
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So this is a force that is going up at the ramp, but the block is moving down the ramp...