Your Tires: Wheels are 1.25 inches in diameter. Fastest speec is 3 ft/second. Ma

Question

Your Tires:

Wheels are 1.25 inches in diameter. Fastest speec is 3 ft/second. Maximum distance to travel is 16 x (18cm).

Convert the dimenstions for the wheel and maximum distance to feet.

A 5% error in disance is allowed. What is the total distance if the 5% error is applied?

Shorter distance with error______

Longer distance with error______

How many times does the wheel turn to travel the maximum distance? If you take into account the 5% error, how does this affect the number of turns of the wheel?

How long does it take to travel the maximum disance at full speed? Is this impacted by the distance error? How?

What is the acceleration needed to travel the maximum distance when starting from a standstill? How is acceleration impacted by the distance error?

Explanation / Answer

your tires:
wheels are 1.25 inches in diameter.
fastest speed is 3ft/sec.
maximum distance to travel is 16 x (18 cm)
1. convert the dimensions for the wheel and maximum distance to feet.
wheel diameter in feet: = 1.25/12 ft
maximum distance in feet: 16*18 = 288 cm
max d = 288/(2.54*12) = 24/2.54 ft
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a 5% error in distance is allowed. what is the total distance if the 5% error is applied?
= max d * 0.95
shorter distance with error: = max d * 0.95
longer distance with error: max d * 1.05
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2. how many times does the wheel turn to travel the maximum distance?
1.25 in = 3.175 cm
Circumference = 3.175*pi cm
# of turns = max d/circumference
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if you take into account the 5% error, how does this affect the number of truns of the wheel? Changes by same percent
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3. how long does it take to travel the maximum distance at full speed?
3 ft/sec = 91.44 cm/sec
t = d/r
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is this impacted by the distance error? how? By the same %age.
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4. what is the acceleration needed to travel the maximum distance when starting from a standstill? Any acceleration > 0 will work, the times depend on the value.
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how is acceleration impacted by the distance error? by the same %age.
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5. examine the pathways below calculate the time to travel each path, taking into account slowing and turning time. also calculate the number of turns of the wheel on each path segment. the star is the finish. corridors are 16.2 cm wide. be specific about the time you allow fro slowing and turning.
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Not enough info, no info given on slowing and turning time.
...............................9.5 ft.
.......................______________________
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......................|......_________....................|
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.............9.5 ft.|.....|_________|...................|
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......................|......______......|...................|
......................|.....|3 ft.......|.....|...................|
......................|.....|............|2.5ft..................|
......................|.....|............|__________*__|
......................|.....|............|.........................|
......................|.....|______|____________|
...................... Start



assume all blocked areas are 16.2 cm wide unless specified.
assume all corridors are 16.2 cm wide,expect for the one containing the star.
which path is the fastest? shortest? why? (do you have to slow more on a sharp turn?)
could you use the number of wheel turn to determine the path of motion?

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