Calculate the centripetal force acting on the car for various radius of curvatur
ID: 1877105 • Letter: C
Question
Calculate the centripetal force acting on the car for various radius of curvature ranging from 0.2 to 1 mile in steps of 0.1 and velocity of car ranging from 20 to 120 miles/hour in steps of 10. (Consider constant mass of vehicle =1200 pounds). Disclaimer: The values of centripetal force may be very high. This is only for academic purposesand may not hold for practical application. Then calculate the maximum velocity of the car on the banked road for varying radius of curvature ranging from 0.2 to 1 mile in steps of 0.1 and the inclination angle ranging from 10° to 40° in steps of 5°.(Consider coefficient of static friction 0.85 and acceleration due to gravity as 78919.11 miles/hr2).
Explanation / Answer
given
v = sqrt(rg(sin(theta) + uk(cos(theta)))/(cos(theta) - uk*sin(theta)))
r ranging from 0.2 to 1 mile in steps of 0.1
v ranging from 20 to 120 mph in steps of 10
m = 1200 pounds
Vmax for 0.2 < v < 1 mile/s
inclination range = 10 to 40 deg in steps of 5 deg
uk = 0.85
g = 78919.11 mil/hr
so
the table for centripital Force
centripital force is given by mv^2/r
r v mv^2/r(pounds mil/hr^2)
0.2 30 5400000
0.2 40 9600000
0.2 50 15000000
0.2 60 21600000
0.2 70 29400000
0.2 80 38400000
0.2 90 48600000
0.2 100 60000000
0.2 110 72600000
0.2 120 86400000
0.3 30 3600000
0.3 40 6400000
0.3 50 10000000
0.3 60 14400000
0.3 70 19600000
0.3 80 25600000
0.3 90 32400000
0.3 100 40000000
0.3 110 48400000
0.3 120 57600000
0.4 30 2700000
0.4 40 4800000
0.4 50 7500000
0.4 60 10800000
0.4 70 14700000
0.4 80 19200000
0.4 90 24300000
0.4 100 30000000
0.4 110 36300000
0.4 120 43200000
0.5 30 2160000
0.5 40 3840000
0.5 50 6000000
0.5 60 8640000
0.5 70 11760000
0.5 80 15360000
0.5 90 19440000
0.5 100 24000000
0.5 110 29040000
0.5 120 34560000
0.6 30 1800000
0.6 40 3200000
0.6 50 5000000
0.6 60 7200000
0.6 70 9800000
0.6 80 12800000
0.6 90 16200000
0.6 100 20000000
0.6 110 24200000
0.6 120 28800000
0.7 30 1542857.143
0.7 40 2742857.143
0.7 50 4285714.286
0.7 60 6171428.571
0.7 70 8400000
0.7 80 10971428.57
0.7 90 13885714.29
0.7 100 17142857.14
0.7 110 20742857.14
0.7 120 24685714.29
0.8 30 1350000
0.8 40 2400000
0.8 50 3750000
0.8 60 5400000
0.8 70 7350000
0.8 80 9600000
0.8 90 12150000
0.8 100 15000000
0.8 110 18150000
0.8 120 21600000
0.9 30 1200000
0.9 40 2133333.333
0.9 50 3333333.333
0.9 60 4800000
0.9 70 6533333.333
0.9 80 8533333.333
0.9 90 10800000
0.9 100 13333333.33
0.9 110 16133333.33
0.9 120 19200000
1 30 1080000
1 40 1920000
1 50 3000000
1 60 4320000
1 70 5880000
1 80 7680000
1 90 9720000
1 100 12000000
1 110 14520000
1 120 17280000
then Vmax data
r theta v^2 Vmax
0.2 10 19055.3369 138.0410696
0.2 15 22849.68177 151.161112
0.2 20 27744.55275 166.5669618
0.2 25 34418.55696 185.5223894
0.2 30 44239.4543 210.331772
0.2 35 60441.63507 245.8488053
0.2 40 92969.57011 304.9091178
0.3 10 28583.00534 169.065092
0.3 15 34274.52265 185.1337966
0.3 20 41616.82913 204.0020322
0.3 25 51627.83545 227.2175949
0.3 30 66359.18146 257.602759
0.3 35 90662.4526 301.1020634
0.3 40 139454.3552 373.4358783
0.4 10 38110.67379 195.2195528
0.4 15 45699.36354 213.7740946
0.4 20 55489.1055 235.5612564
0.4 25 68837.11393 262.3682792
0.4 30 88478.90861 297.4540445
0.4 35 120883.2701 347.6827148
0.4 40 185939.1402 431.2066097
0.5 10 47638.34224 218.2620953
0.5 15 57124.20442 239.0067037
0.5 20 69361.38188 263.3654911
0.5 25 86046.39241 293.3366537
0.5 30 110598.6358 332.5637319
0.5 35 151104.0877 388.7210924
0.5 40 232423.9253 482.1036458
0.6 10 57166.01069 239.0941461
0.6 15 68549.04531 261.818726
0.6 20 83233.65825 288.5024406
0.6 25 103255.6709 321.3342044
0.6 30 132718.3629 364.3053155
0.6 35 181324.9052 425.8226218
0.6 40 278908.7103 528.1180837
0.7 10 66693.67913 258.2511939
0.7 15 79973.88619 282.7965456
0.7 20 97105.93463 311.6182514
0.7 25 120464.9494 347.0806093
0.7 30 154838.0901 393.4947142
0.7 35 211545.7227 459.9409992
0.7 40 325393.4954 570.4327264
0.8 10 76221.34758 276.0821392
0.8 15 91398.72708 302.3222239
0.8 20 110978.211 333.1339235
0.8 25 137674.2279 371.0447788
0.8 30 176957.8172 420.663544
0.8 35 241766.5403 491.6976106
0.8 40 371878.2804 609.8182356
0.9 10 85749.01603 292.8293292
0.9 15 102823.568 320.661142
0.9 20 124850.4874 353.3418846
0.9 25 154883.5063 393.5524188
0.9 30 199077.5444 446.1810668
0.9 35 271987.3578 521.5240721
0.9 40 418363.0655 646.8099145
1 10 95276.68448 308.6692153
1 15 114248.4088 338.0065219
1 20 138722.7638 372.4550493
1 25 172092.7848 414.840674
1 30 221197.2715 470.31614
1 35 302208.1753 549.7346408
1 40 464847.8506 681.7975143
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