The formula to calculate the Force of Friction (\(F_f\)) is:
\[ F_f = \frac{M_c \cdot g \cdot \sin(\theta_i)}{3} \]
Where:
Force of Friction refers to the force generated by two surfaces that contact and slide against each other.
Mass of Cylinder is the property of a body that is a measure of its inertia, which is commonly taken as a measure of the amount of material it contains.
Acceleration Due to Gravity is acceleration gained by an object because of gravitational force.
Angle of Inclination is formed by the inclination of one line to another; measured in degrees or radians.
Let's assume the following values:
Using the formula:
\[ F_f = \frac{M_c \cdot g \cdot \sin(\theta_i)}{3} \]
Evaluating:
\[ F_f = \frac{9.6 \cdot 9.8 \cdot \sin(0.785398163397301)}{3} \]
The Force of Friction is 22.1749 N.
| Mass (kg) | Gravity (m/s²) | Angle (rad) | Force of Friction (N) |
|---|---|---|---|
| 5 | 9.5 | 0.5 | 7.5909 |
| 5 | 9.5 | 0.6 | 8.9402 |
| 5 | 9.5 | 0.7 | 10.2001 |
| 5 | 9.5 | 0.8 | 11.3581 |
| 5 | 9.5 | 0.9 | 12.4027 |
| 5 | 9.5 | 1 | 13.3233 |
| 5 | 9.6 | 0.5 | 7.6708 |
| 5 | 9.6 | 0.6 | 9.0343 |
| 5 | 9.6 | 0.7 | 10.3075 |
| 5 | 9.6 | 0.8 | 11.4777 |
| 5 | 9.6 | 0.9 | 12.5332 |
| 5 | 9.6 | 1 | 13.4635 |
| 5 | 9.7 | 0.5 | 7.7507 |
| 5 | 9.7 | 0.6 | 9.1284 |
| 5 | 9.7 | 0.7 | 10.4149 |
| 5 | 9.7 | 0.8 | 11.5973 |
| 5 | 9.7 | 0.9 | 12.6638 |
| 5 | 9.7 | 1 | 13.6038 |
| 5 | 9.8 | 0.5 | 7.8306 |
| 5 | 9.8 | 0.6 | 9.2225 |
| 5 | 9.8 | 0.7 | 10.5222 |
| 5 | 9.8 | 0.8 | 11.7168 |
| 5 | 9.8 | 0.9 | 12.7943 |
| 5 | 9.8 | 1 | 13.7440 |
| 5 | 9.9 | 0.5 | 7.9105 |
| 5 | 9.9 | 0.6 | 9.3166 |
| 5 | 9.9 | 0.7 | 10.6296 |
| 5 | 9.9 | 0.8 | 11.8364 |
| 5 | 9.9 | 0.9 | 12.9249 |
| 5 | 9.9 | 1 | 13.8843 |
| 5 | 10 | 0.5 | 7.9904 |
| 5 | 10 | 0.6 | 9.4107 |
| 5 | 10 | 0.7 | 10.7370 |
| 5 | 10 | 0.8 | 11.9559 |
| 5 | 10 | 0.9 | 13.0554 |
| 5 | 10 | 1 | 14.0245 |
| 6 | 9.5 | 0.5 | 9.1091 |
| 6 | 9.5 | 0.6 | 10.7282 |
| 6 | 9.5 | 0.7 | 12.2401 |
| 6 | 9.5 | 0.8 | 13.6298 |
| 6 | 9.5 | 0.9 | 14.8832 |
| 6 | 9.5 | 1 | 15.9879 |
| 6 | 9.6 | 0.5 | 9.2050 |
| 6 | 9.6 | 0.6 | 10.8411 |
| 6 | 9.6 | 0.7 | 12.3690 |
| 6 | 9.6 | 0.8 | 13.7732 |
| 6 | 9.6 | 0.9 | 15.0399 |
| 6 | 9.6 | 1 | 16.1562 |
| 6 | 9.7 | 0.5 | 9.3009 |
| 6 | 9.7 | 0.6 | 10.9541 |
| 6 | 9.7 | 0.7 | 12.4978 |
| 6 | 9.7 | 0.8 | 13.9167 |
| 6 | 9.7 | 0.9 | 15.1965 |
| 6 | 9.7 | 1 | 16.3245 |
| 6 | 9.8 | 0.5 | 9.3967 |
| 6 | 9.8 | 0.6 | 11.0670 |
| 6 | 9.8 | 0.7 | 12.6267 |
| 6 | 9.8 | 0.8 | 14.0602 |
| 6 | 9.8 | 0.9 | 15.3532 |
| 6 | 9.8 | 1 | 16.4928 |
| 6 | 9.9 | 0.5 | 9.4926 |
| 6 | 9.9 | 0.6 | 11.1799 |
| 6 | 9.9 | 0.7 | 12.7555 |
| 6 | 9.9 | 0.8 | 14.2037 |
| 6 | 9.9 | 0.9 | 15.5099 |
| 6 | 9.9 | 1 | 16.6611 |
| 6 | 10 | 0.5 | 9.5885 |
| 6 | 10 | 0.6 | 11.2928 |
| 6 | 10 | 0.7 | 12.8844 |
| 6 | 10 | 0.8 | 14.3471 |
| 6 | 10 | 0.9 | 15.6665 |
| 6 | 10 | 1 | 16.8294 |
| 7 | 9.5 | 0.5 | 10.6273 |
| 7 | 9.5 | 0.6 | 12.5162 |
| 7 | 9.5 | 0.7 | 14.2802 |
| 7 | 9.5 | 0.8 | 15.9014 |
| 7 | 9.5 | 0.9 | 17.3637 |
| 7 | 9.5 | 1 | 18.6526 |
| 7 | 9.6 | 0.5 | 10.7391 |
| 7 | 9.6 | 0.6 | 12.6480 |
| 7 | 9.6 | 0.7 | 14.4305 |
| 7 | 9.6 | 0.8 | 16.0688 |
| 7 | 9.6 | 0.9 | 17.5465 |
| 7 | 9.6 | 1 | 18.8490 |
| 7 | 9.7 | 0.5 | 10.8510 |
| 7 | 9.7 | 0.6 | 12.7797 |
| 7 | 9.7 | 0.7 | 14.5808 |
| 7 | 9.7 | 0.8 | 16.2362 |
| 7 | 9.7 | 0.9 | 17.7293 |
| 7 | 9.7 | 1 | 19.0453 |
| 7 | 9.8 | 0.5 | 10.9629 |
| 7 | 9.8 | 0.6 | 12.9115 |
| 7 | 9.8 | 0.7 | 14.7311 |
| 7 | 9.8 | 0.8 | 16.4035 |
| 7 | 9.8 | 0.9 | 17.9121 |
| 7 | 9.8 | 1 | 19.2416 |
| 7 | 9.9 | 0.5 | 11.0747 |
| 7 | 9.9 | 0.6 | 13.0432 |
| 7 | 9.9 | 0.7 | 14.8814 |
| 7 | 9.9 | 0.8 | 16.5709 |
| 7 | 9.9 | 0.9 | 18.0949 |
| 7 | 9.9 | 1 | 19.4380 |
| 7 | 10 | 0.5 | 11.1866 |
| 7 | 10 | 0.6 | 13.1750 |
| 7 | 10 | 0.7 | 15.0317 |
| 7 | 10 | 0.8 | 16.7383 |
| 7 | 10 | 0.9 | 18.2776 |
| 7 | 10 | 1 | 19.6343 |
| 8 | 9.5 | 0.5 | 12.1454 |
| 8 | 9.5 | 0.6 | 14.3043 |
| 8 | 9.5 | 0.7 | 16.3202 |
| 8 | 9.5 | 0.8 | 18.1730 |
| 8 | 9.5 | 0.9 | 19.8443 |
| 8 | 9.5 | 1 | 21.3173 |
| 8 | 9.6 | 0.5 | 12.2733 |
| 8 | 9.6 | 0.6 | 14.4548 |
| 8 | 9.6 | 0.7 | 16.4920 |
| 8 | 9.6 | 0.8 | 18.3643 |
| 8 | 9.6 | 0.9 | 20.0532 |
| 8 | 9.6 | 1 | 21.5417 |
| 8 | 9.7 | 0.5 | 12.4011 |
| 8 | 9.7 | 0.6 | 14.6054 |
| 8 | 9.7 | 0.7 | 16.6638 |
| 8 | 9.7 | 0.8 | 18.5556 |
| 8 | 9.7 | 0.9 | 20.2621 |
| 8 | 9.7 | 1 | 21.7660 |
| 8 | 9.8 | 0.5 | 12.5290 |
| 8 | 9.8 | 0.6 | 14.7560 |
| 8 | 9.8 | 0.7 | 16.8356 |
| 8 | 9.8 | 0.8 | 18.7469 |
| 8 | 9.8 | 0.9 | 20.4709 |
| 8 | 9.8 | 1 | 21.9904 |
| 8 | 9.9 | 0.5 | 12.6568 |
| 8 | 9.9 | 0.6 | 14.9066 |
| 8 | 9.9 | 0.7 | 17.0073 |
| 8 | 9.9 | 0.8 | 18.9382 |
| 8 | 9.9 | 0.9 | 20.6798 |
| 8 | 9.9 | 1 | 22.2148 |
| 8 | 10 | 0.5 | 12.7847 |
| 8 | 10 | 0.6 | 15.0571 |
| 8 | 10 | 0.7 | 17.1791 |
| 8 | 10 | 0.8 | 19.1295 |
| 8 | 10 | 0.9 | 20.8887 |
| 8 | 10 | 1 | 22.4392 |
| 9 | 9.5 | 0.5 | 13.6636 |
| 9 | 9.5 | 0.6 | 16.0923 |
| 9 | 9.5 | 0.7 | 18.3602 |
| 9 | 9.5 | 0.8 | 20.4446 |
| 9 | 9.5 | 0.9 | 22.3248 |
| 9 | 9.5 | 1 | 23.9819 |
| 9 | 9.6 | 0.5 | 13.8075 |
| 9 | 9.6 | 0.6 | 16.2617 |
| 9 | 9.6 | 0.7 | 18.5535 |
| 9 | 9.6 | 0.8 | 20.6599 |
| 9 | 9.6 | 0.9 | 22.5598 |
| 9 | 9.6 | 1 | 24.2344 |
| 9 | 9.7 | 0.5 | 13.9513 |
| 9 | 9.7 | 0.6 | 16.4311 |
| 9 | 9.7 | 0.7 | 18.7467 |
| 9 | 9.7 | 0.8 | 20.8751 |
| 9 | 9.7 | 0.9 | 22.7948 |
| 9 | 9.7 | 1 | 24.4868 |
| 9 | 9.8 | 0.5 | 14.0951 |
| 9 | 9.8 | 0.6 | 16.6005 |
| 9 | 9.8 | 0.7 | 18.9400 |
| 9 | 9.8 | 0.8 | 21.0903 |
| 9 | 9.8 | 0.9 | 23.0298 |
| 9 | 9.8 | 1 | 24.7392 |
| 9 | 9.9 | 0.5 | 14.2389 |
| 9 | 9.9 | 0.6 | 16.7699 |
| 9 | 9.9 | 0.7 | 19.1333 |
| 9 | 9.9 | 0.8 | 21.3055 |
| 9 | 9.9 | 0.9 | 23.2648 |
| 9 | 9.9 | 1 | 24.9917 |
| 9 | 10 | 0.5 | 14.3828 |
| 9 | 10 | 0.6 | 16.9393 |
| 9 | 10 | 0.7 | 19.3265 |
| 9 | 10 | 0.8 | 21.5207 |
| 9 | 10 | 0.9 | 23.4998 |
| 9 | 10 | 1 | 25.2441 |
| 10 | 9.5 | 0.5 | 15.1818 |
| 10 | 9.5 | 0.6 | 17.8803 |
| 10 | 9.5 | 0.7 | 20.4002 |
| 10 | 9.5 | 0.8 | 22.7163 |
| 10 | 9.5 | 0.9 | 24.8054 |
| 10 | 9.5 | 1 | 26.6466 |
| 10 | 9.6 | 0.5 | 15.3416 |
| 10 | 9.6 | 0.6 | 18.0686 |
| 10 | 9.6 | 0.7 | 20.6150 |
| 10 | 9.6 | 0.8 | 22.9554 |
| 10 | 9.6 | 0.9 | 25.0665 |
| 10 | 9.6 | 1 | 26.9271 |
| 10 | 9.7 | 0.5 | 15.5014 |
| 10 | 9.7 | 0.6 | 18.2568 |
| 10 | 9.7 | 0.7 | 20.8297 |
| 10 | 9.7 | 0.8 | 23.1945 |
| 10 | 9.7 | 0.9 | 25.3276 |
| 10 | 9.7 | 1 | 27.2076 |
| 10 | 9.8 | 0.5 | 15.6612 |
| 10 | 9.8 | 0.6 | 18.4450 |
| 10 | 9.8 | 0.7 | 21.0444 |
| 10 | 9.8 | 0.8 | 23.4336 |
| 10 | 9.8 | 0.9 | 25.5887 |
| 10 | 9.8 | 1 | 27.4881 |
| 10 | 9.9 | 0.5 | 15.8210 |
| 10 | 9.9 | 0.6 | 18.6332 |
| 10 | 9.9 | 0.7 | 21.2592 |
| 10 | 9.9 | 0.8 | 23.6728 |
| 10 | 9.9 | 0.9 | 25.8498 |
| 10 | 9.9 | 1 | 27.7685 |
| 10 | 10 | 0.5 | 15.9809 |
| 10 | 10 | 0.6 | 18.8214 |
| 10 | 10 | 0.7 | 21.4739 |
| 10 | 10 | 0.8 | 23.9119 |
| 10 | 10 | 0.9 | 26.1109 |
| 10 | 10 | 1 | 28.0490 |
| 11 | 9.5 | 0.5 | 16.7000 |
| 11 | 9.5 | 0.6 | 19.6684 |
| 11 | 9.5 | 0.7 | 22.4402 |
| 11 | 9.5 | 0.8 | 24.9879 |
| 11 | 9.5 | 0.9 | 27.2859 |
| 11 | 9.5 | 1 | 29.3112 |
| 11 | 9.6 | 0.5 | 16.8758 |
| 11 | 9.6 | 0.6 | 19.8754 |
| 11 | 9.6 | 0.7 | 22.6765 |
| 11 | 9.6 | 0.8 | 25.2509 |
| 11 | 9.6 | 0.9 | 27.5731 |
| 11 | 9.6 | 1 | 29.6198 |
| 11 | 9.7 | 0.5 | 17.0516 |
| 11 | 9.7 | 0.6 | 20.0825 |
| 11 | 9.7 | 0.7 | 22.9127 |
| 11 | 9.7 | 0.8 | 25.5140 |
| 11 | 9.7 | 0.9 | 27.8603 |
| 11 | 9.7 | 1 | 29.9283 |
| 11 | 9.8 | 0.5 | 17.2274 |
| 11 | 9.8 | 0.6 | 20.2895 |
| 11 | 9.8 | 0.7 | 23.1489 |
| 11 | 9.8 | 0.8 | 25.7770 |
| 11 | 9.8 | 0.9 | 28.1475 |
| 11 | 9.8 | 1 | 30.2369 |
| 11 | 9.9 | 0.5 | 17.4031 |
| 11 | 9.9 | 0.6 | 20.4965 |
| 11 | 9.9 | 0.7 | 23.3851 |
| 11 | 9.9 | 0.8 | 26.0400 |
| 11 | 9.9 | 0.9 | 28.4348 |
| 11 | 9.9 | 1 | 30.5454 |
| 11 | 10 | 0.5 | 17.5789 |
| 11 | 10 | 0.6 | 20.7036 |
| 11 | 10 | 0.7 | 23.6213 |
| 11 | 10 | 0.8 | 26.3031 |
| 11 | 10 | 0.9 | 28.7220 |
| 11 | 10 | 1 | 30.8539 |
| 12 | 9.5 | 0.5 | 18.2182 |
| 12 | 9.5 | 0.6 | 21.4564 |
| 12 | 9.5 | 0.7 | 24.4803 |
| 12 | 9.5 | 0.8 | 27.2595 |
| 12 | 9.5 | 0.9 | 29.7664 |
| 12 | 9.5 | 1 | 31.9759 |
| 12 | 9.6 | 0.5 | 18.4099 |
| 12 | 9.6 | 0.6 | 21.6823 |
| 12 | 9.6 | 0.7 | 24.7380 |
| 12 | 9.6 | 0.8 | 27.5465 |
| 12 | 9.6 | 0.9 | 30.0798 |
| 12 | 9.6 | 1 | 32.3125 |
| 12 | 9.7 | 0.5 | 18.6017 |
| 12 | 9.7 | 0.6 | 21.9081 |
| 12 | 9.7 | 0.7 | 24.9956 |
| 12 | 9.7 | 0.8 | 27.8334 |
| 12 | 9.7 | 0.9 | 30.3931 |
| 12 | 9.7 | 1 | 32.6491 |
| 12 | 9.8 | 0.5 | 18.7935 |
| 12 | 9.8 | 0.6 | 22.1340 |
| 12 | 9.8 | 0.7 | 25.2533 |
| 12 | 9.8 | 0.8 | 28.1204 |
| 12 | 9.8 | 0.9 | 30.7064 |
| 12 | 9.8 | 1 | 32.9857 |
| 12 | 9.9 | 0.5 | 18.9853 |
| 12 | 9.9 | 0.6 | 22.3598 |
| 12 | 9.9 | 0.7 | 25.5110 |
| 12 | 9.9 | 0.8 | 28.4073 |
| 12 | 9.9 | 0.9 | 31.0197 |
| 12 | 9.9 | 1 | 33.3223 |
| 12 | 10 | 0.5 | 19.1770 |
| 12 | 10 | 0.6 | 22.5857 |
| 12 | 10 | 0.7 | 25.7687 |
| 12 | 10 | 0.8 | 28.6942 |
| 12 | 10 | 0.9 | 31.3331 |
| 12 | 10 | 1 | 33.6588 |
| 13 | 9.5 | 0.5 | 19.7364 |
| 13 | 9.5 | 0.6 | 23.2444 |
| 13 | 9.5 | 0.7 | 26.5203 |
| 13 | 9.5 | 0.8 | 29.5312 |
| 13 | 9.5 | 0.9 | 32.2470 |
| 13 | 9.5 | 1 | 34.6406 |
| 13 | 9.6 | 0.5 | 19.9441 |
| 13 | 9.6 | 0.6 | 23.4891 |
| 13 | 9.6 | 0.7 | 26.7995 |
| 13 | 9.6 | 0.8 | 29.8420 |
| 13 | 9.6 | 0.9 | 32.5864 |
| 13 | 9.6 | 1 | 35.0052 |
| 13 | 9.7 | 0.5 | 20.1519 |
| 13 | 9.7 | 0.6 | 23.7338 |
| 13 | 9.7 | 0.7 | 27.0786 |
| 13 | 9.7 | 0.8 | 30.1529 |
| 13 | 9.7 | 0.9 | 32.9258 |
| 13 | 9.7 | 1 | 35.3698 |
| 13 | 9.8 | 0.5 | 20.3596 |
| 13 | 9.8 | 0.6 | 23.9785 |
| 13 | 9.8 | 0.7 | 27.3578 |
| 13 | 9.8 | 0.8 | 30.4637 |
| 13 | 9.8 | 0.9 | 33.2653 |
| 13 | 9.8 | 1 | 35.7345 |
| 13 | 9.9 | 0.5 | 20.5674 |
| 13 | 9.9 | 0.6 | 24.2232 |
| 13 | 9.9 | 0.7 | 27.6369 |
| 13 | 9.9 | 0.8 | 30.7746 |
| 13 | 9.9 | 0.9 | 33.6047 |
| 13 | 9.9 | 1 | 36.0991 |
| 13 | 10 | 0.5 | 20.7751 |
| 13 | 10 | 0.6 | 24.4678 |
| 13 | 10 | 0.7 | 27.9161 |
| 13 | 10 | 0.8 | 31.0854 |
| 13 | 10 | 0.9 | 33.9442 |
| 13 | 10 | 1 | 36.4637 |
| 14 | 9.5 | 0.5 | 21.2545 |
| 14 | 9.5 | 0.6 | 25.0325 |
| 14 | 9.5 | 0.7 | 28.5603 |
| 14 | 9.5 | 0.8 | 31.8028 |
| 14 | 9.5 | 0.9 | 34.7275 |
| 14 | 9.5 | 1 | 37.3052 |
| 14 | 9.6 | 0.5 | 21.4783 |
| 14 | 9.6 | 0.6 | 25.2960 |
| 14 | 9.6 | 0.7 | 28.8610 |
| 14 | 9.6 | 0.8 | 32.1376 |
| 14 | 9.6 | 0.9 | 35.0930 |
| 14 | 9.6 | 1 | 37.6979 |
| 14 | 9.7 | 0.5 | 21.7020 |
| 14 | 9.7 | 0.6 | 25.5595 |
| 14 | 9.7 | 0.7 | 29.1616 |
| 14 | 9.7 | 0.8 | 32.4723 |
| 14 | 9.7 | 0.9 | 35.4586 |
| 14 | 9.7 | 1 | 38.0906 |
| 14 | 9.8 | 0.5 | 21.9257 |
| 14 | 9.8 | 0.6 | 25.8230 |
| 14 | 9.8 | 0.7 | 29.4622 |
| 14 | 9.8 | 0.8 | 32.8071 |
| 14 | 9.8 | 0.9 | 35.8242 |
| 14 | 9.8 | 1 | 38.4833 |
| 14 | 9.9 | 0.5 | 22.1495 |
| 14 | 9.9 | 0.6 | 26.0865 |
| 14 | 9.9 | 0.7 | 29.7629 |
| 14 | 9.9 | 0.8 | 33.1419 |
| 14 | 9.9 | 0.9 | 36.1897 |
| 14 | 9.9 | 1 | 38.8760 |
| 14 | 10 | 0.5 | 22.3732 |
| 14 | 10 | 0.6 | 26.3500 |
| 14 | 10 | 0.7 | 30.0635 |
| 14 | 10 | 0.8 | 33.4766 |
| 14 | 10 | 0.9 | 36.5553 |
| 14 | 10 | 1 | 39.2686 |
| 15 | 9.5 | 0.5 | 22.7727 |
| 15 | 9.5 | 0.6 | 26.8205 |
| 15 | 9.5 | 0.7 | 30.6003 |
| 15 | 9.5 | 0.8 | 34.0744 |
| 15 | 9.5 | 0.9 | 37.2080 |
| 15 | 9.5 | 1 | 39.9699 |
| 15 | 9.6 | 0.5 | 23.0124 |
| 15 | 9.6 | 0.6 | 27.1028 |
| 15 | 9.6 | 0.7 | 30.9224 |
| 15 | 9.6 | 0.8 | 34.4331 |
| 15 | 9.6 | 0.9 | 37.5997 |
| 15 | 9.6 | 1 | 40.3906 |
| 15 | 9.7 | 0.5 | 23.2521 |
| 15 | 9.7 | 0.6 | 27.3852 |
| 15 | 9.7 | 0.7 | 31.2446 |
| 15 | 9.7 | 0.8 | 34.7918 |
| 15 | 9.7 | 0.9 | 37.9914 |
| 15 | 9.7 | 1 | 40.8113 |
| 15 | 9.8 | 0.5 | 23.4919 |
| 15 | 9.8 | 0.6 | 27.6675 |
| 15 | 9.8 | 0.7 | 31.5667 |
| 15 | 9.8 | 0.8 | 35.1504 |
| 15 | 9.8 | 0.9 | 38.3830 |
| 15 | 9.8 | 1 | 41.2321 |
| 15 | 9.9 | 0.5 | 23.7316 |
| 15 | 9.9 | 0.6 | 27.9498 |
| 15 | 9.9 | 0.7 | 31.8888 |
| 15 | 9.9 | 0.8 | 35.5091 |
| 15 | 9.9 | 0.9 | 38.7747 |
| 15 | 9.9 | 1 | 41.6528 |
| 15 | 10 | 0.5 | 23.9713 |
| 15 | 10 | 0.6 | 28.2321 |
| 15 | 10 | 0.7 | 32.2109 |
| 15 | 10 | 0.8 | 35.8678 |
| 15 | 10 | 0.9 | 39.1663 |
| 15 | 10 | 1 | 42.0735 |