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Hi everyone.
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What we're going to be looking at is a problem that combines both the concepts of newton's second law of f equals ma and also the conservation of energy.
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So the way we're going to be doing this is by first using newton's second law and the free body diagrams to determine accelerations and use those accelerations in our equations for conservation of energy and kinematics.
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So what we're what's given to us is we have a suitcase at point a that has a way.
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Weight of 40 pounds and an initial velocity of 10 feet per second, which comes down this hill from a to b and lands at point c as designated here.
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We know that the coefficient of friction on the path a .b is equal to 0 .2.
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And we also know that the angle of the slope a .b is 30 degrees and that the point b is at a height of 4 feet.
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We also know the distance from a to b is equal.
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With a 20 feet.
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What we're asked to solve for is the distance r, which is the point at which the suitcase hits the ground, which is point c.
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And we're also asked to solve for the time that it takes to reach that point.
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So what we're going to do first is draw our free body diagram.
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What we can do is we can draw our suitcase that is on the slope, which again, as you recall, has an angle equal to 30 degrees.
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This suitcase has a normal force coming from the slope and a weight force that is acting straight down.
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And by resolving the components in the coordinate that aligns with our acceleration, which is this direction here.
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So this is this is x and this is y.
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We see that the normal force is equal to w cosine theta, which is equal to mg, coast theta.
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And this was our weight, net force balance in the wide direction.
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Next, what we can do is draw our free body diagram for the forces that are acting in the x direction.
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And we can just go ahead and draw our suitcase, which is again at an angle of 30 degrees.
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So if we look at the forces that are acting in our x direction, we see we have a component of the weight force that acts in the x direction...