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course PHY 241
08/31/20115:21 AM
Let's apply the definition of average rate to another situation. Answer the following, inserting your answer to each question between the **** line and the #$&* line. You should provide your detailed reasoning on each question, along the lines of the reasoning presented in the preceding examples:
If we turn on a tap at 11:24 a.m. and direct it into an empty 5-gallon bucket, and find that the bucket first reaches the full level at 11:28 a.m., at what average rate is water flowing into the bucket with respect to clock time?
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5 gallons/4 minutes
1.25 gallons/ minute
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Specifically how does the definition of average rate apply to this situation? What is the A quantity? What is the B quantity?
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The basic definition leads to this: How many gallons pour into the bucket per minute? A is the quantity of water, B is the time.
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What event begins the interval, and what event ends it?
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Turning on the faucet begins the interval, and the bucket being full ends it.
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Answer the following as well:
Water flows through household plumbing at a typical average rate of about 3 gallons per minute. Had the tap been turned on at 11:28, and had water flowed at this rate, when would the bucket have been full?
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5 Gallons * minute/3gallons = 5/3 minutes
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And answer the following:
A ball rolls from rest down a 30 cm ramp in 6 'beats'. Starting with the definition of rate, reason out your answers, showing the details of your reasoning:
What is the average rate at which the position of the ball changes during the interval starting with release and ending when the ball passes the end of the ramp?
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5 cm
If the ball takes 6 beats to travel 30 cm, then the average ratio would be 30/6 which is equal to 5
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How fast do you conjecture that the ball is probably rolling when it reaches the end of the ramp?
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10 cm per beat
if the average velocity was 5 cm per beat, and it started from 0 cm per beat, then to get the appropriate average we need twice the average to get the appropriate value.
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How quickly would you therefore conclude the velocity of the ball is changing?
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5 cm/3 beat
if it takes 6 beats for the ball to be travelling 10 cm per beat, then the ratio of speed to beats looks like this 10 cm/ 6 beat which reduces to 5 cm/ 3 beats
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@& Close. But it's (10 cm/beat) / (6 beats), not (10 cm) / (6 beats).*@
What is the average rate at which the velocity of the ball changes during the interval starting with release and ending when the ball passes the end of the ramp?
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same as above
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At this point of the course there are no formulas, only these concepts and definitions. These definitions lead to formulas, but for right now we aren't going to pollute your sensibilities with formulas that will invite you to bypass understanding.
... calculating change in A given ave rate and change in B ... when would the bucket be full at 3 gal / min
... leading to velocity and acceleration, the former being pretty easy to understand, the second not much so
At this point there are no formulas, only these concepts and definitions. These definitions lead to formulas, but for right now we aren't going to pollute your sensibilities with formulas that will invite you to bypass understanding.
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@& Good work.
You had an error on units on the last couple of questions. Be sure you see my notes.
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