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Cart tipping problem

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I am to solve a tipping problem of a 4-wheeled cart, weighing 36 kg, and being pushed to move in a range of between 1 and 6 m/sec. When the cart is moving at constant velocity within this range, the front two wheels suddenly encounter a permanent barrier and are stopped instantaneuosly. The cart is to be redesigned for no or minimal tipping-up of the back wheels over this operting range, see drawing.

How do you decribe the dynamics of the cart? I realize I can sum the moments about the front axle of the cart, with position vectors times the cart's weight from the center of mass, and the normal forces acting on the cart wheels. What I don't understand is how to express the cart's momentum / kinetic energy as a force. The cart is moving at constant velocity, and the stop is instantaneous. I want to design the cart so that it does not tip within this speed range, any thoughts on how to approach?

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https://brainmass.com/engineering/mining-engineering/cart-tipping-problem-35706

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UPDATE:
Student Comment:
I was grateful that the response came in well before the deadline, so that I had time to review it fully. While he did solve the problem, here were a few areas where I still have questions and would have liked a capability to ask them. For example, how do you define the magnitude of force F? Why is the tipping point at point A, rather than the point where the wheel center makes contact with the obstruction? If I could get a response to these thoughts, it would aid my understanding. There was also learning I gained from viewing his solution that he did not state- for example, the easiest way to changethe cart is to make the wheels bigger, so that (h-c) is ...

Solution Summary

The solution is provided in an attachment with step-by-step answers which include explanations, diagrams and equations for a total of 750-800 words. Additional feedback in regard to the student's query about the answer is also given.

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Statdisk

Using Statdisk 10.4 version

1) Captopril is a drug designed to lower systolic blood pressure. When subjects were tested with this drug, their systolic blood pressure readings were measured before and after the drug was taken, with the results given in the accompanying table. Is there sufficient evidence to support the claim that the drug has an effect? Does Captopril appear to lower systolic blood pressure?

Subject a b c d e f g h i j k l
Before 200 174 198 170 179 182 193 209 185 155 169 210
after 191 170 177 167 159 151 176 183 159 145 146 177

Test statistic:78
Critical Value:17
Conclusion: We do not accept the claim that the drug has an effect.

2)When the author visited Ireland, he recorded the ages of randomly selected passenger cars and randomly selected taxis. The ages are listed below. Use a 0.05 significance level to test the claim that there is a difference between the median age of a Dublin car and the median age of a Ireland taxi. We might expect the taxis would be newer, but what do the results suggest?

Cars Taxis
4 0 8 11 14 3 4 4 3 5 8 8 3 8 4 3 3 6 11
8 3 3 7 4 6 6 1 8 2 15 7 7 6 9 5 10 8 4 3 4
11 4 1 6 1 8

H0 median 1 = median 2a
H1 median 1 not equal to median 2

TS

Critical value: -1.960

Conclusion: Do not reject H0, there is not sufficient evidence to support the claim that median 1 not equal to median 2.

The results do not suggest that taxis are newer. The median age for the cars was lower.

3) Carts were purchased and crashed into a fixed barrier at 35 mi and measurements were record for the driver. Using the sample data listed to test for differences in head injury measurements among the four weight categories. Is there sufficient evidence to conclude that head injury measurements for the four car weight categories are not all the same? Do the data suggest that heavier cars are safer in a crash?

Subcompact 681 428 917 898 420
compact 643 655 442 514 525
Midsize 469 727 525 454 259
Full size 384 656 602 687 360

Test statistic:
Critical Value:
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4) Students of the author collected sample data consisting of amounts of restaurant bills and the corresponding tip amounts. The data are listed below. Use rank correlation to determine whether there is a correlation between the amount of the bill and the amount of the tip.

Bill 33.46 50.68 87.92 98.84 63.60 107.34
Tip 5.50 5.00 8.08 17.00 12.00 16.00

Test statistic:
Critical value:
Conclusion:

5) For a recent sequence of presidential elections, the political party of the winner is indicated by D for democrat and R for republican. Does it appear that we elect Democrat and republican candidates in a sequence that is random?

R R D R D R R R R D D R R R D D D
D D R R D D R R D R R R D D R R

Test statistic:
Critical value:
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6)Six couple?s leaves a 15% tip. A week later the same couples decide to scramble their tips. Let?s explore the effects of these two events on rank correlation.

Enter the following data in columns 1 through 3 of the Statdisk, and observe the effect on the spearman rank correlation coefficient. Use a 0.05 significance level.

Bill Regular Tips first visit Scrambled Tips second visit
30.90 4.75 7.00
55.89 8.00 10.00
101.15 15.00 12.00
78.80 12.00 15.00
6750 10.00 8.00
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First visit: Regular tips
Using the bill amounts and the tip amounts from the first visit, find the rank correlation coefficient rs:

What do you conclude:

Second visit: Scramble tips
Using the bill amounts and the tip amounts from the second visit, find the rank correlation coefficient rs:

What do you conclude:

What do the results from the events indicate about rank correlation?

Suppose the one couple feels exceptionally generous and changes their tip from $4.75 to $500. That tip of $500.00 clearly becomes an outlier. After replacing both values of $4.75 in the above table by values of $500, repeat the analyses and enter the results below.

First visit: Regular tips
Using the bill amounts and the tip amounts from the first visit, find the rank correlation coefficient rs:

What do you conclude:

Second visit: Scramble tips
Using the bill amounts and the tip amounts from the second visit, find the rank correlation coefficient rs:

What do you conclude:

What do these new results indicate about the effect that an outlier has on rank correlation?

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