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tip In the above figure the block is just on the verge of tipping: W and N act through point A and thus exert zero torque about point A. The incline angle, Otip, is the incline angle beyond which the block will tip, since increasing the angle beyond Orip will move the CG beyond where there is a point of support below it, as in the previous figure. It is not difficult to show, using some geometry and trigonometry, that 0tip is given by Orip = tan' (w/ h) (1) Equation (1) agrees with our intuition: If the block is short and wide (h small, w large) the block will be more difficult to tip (Otip is large) and if the block is tall and narrow (h large, w small) the block will be easier to tip (Otip is small). It is now not difficult to see why the automotive industry defines a safety factor describing how easily a vehicle will rollover as (roughly) vehicle width / vehicle height. The larger this safety factor is, the more resistant the vehicle is to rolling: Short and wide vehicles can take curves at high speeds without rolling, while tall and narrow vehicles cannot. While the torque responsible for tipping a vehicle going around a curve is different than in the case of the block on the incline, the principles involving torques that stabilize and de-stabilize the vehicle to rotation are the same.

tip In the above figure the block is just on the verge of tipping: W and N act through point A and thus exert zero torque about point A. The incline angle, Otip, is the incline angle beyond which the block will tip, since increasing the angle beyond Orip will move the CG beyond where there is a point of support below it, as in the previous figure. It is not difficult to show, using some geometry and trigonometry, that 0tip is given by Orip = tan' (w/ h) (1) Equation (1) agrees with our intuition: If the block is short and wide (h small, w large) the block will be more difficult to tip (Otip is large) and if the block is tall and narrow (h large, w small) the block will be easier to tip (Otip is small). It is now not difficult to see why the automotive industry defines a safety factor describing how easily a vehicle will rollover as (roughly) vehicle width / vehicle height. The larger this safety factor is, the more resistant the vehicle is to rolling: Short and wide vehicles can take curves at high speeds without rolling, while tall and narrow vehicles cannot. While the torque responsible for tipping a vehicle going around a curve is different than in the case of the block on the incline, the principles involving torques that stabilize and de-stabilize the vehicle to rotation are the same.

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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Now consider the figure shown below. N CG -A tip In the above figure the block is just on the verge of tipping: W and N act through point A and thus exert zero torque about point A. The incline angle, Otip, is the incline angle beyond which the block will tip, since increasing the angle beyond Otip will move the CG beyond where there is a point of support below it, as in the previous figure. It is not difficult to show, using some geometry and trigonometry, that Otip is given by Orip = tan' (w / h) (1) Equation (1) agrees with our intuition: If the block is short and wide (h small, w large) the block will be more difficult to tip (Otip is large) and if the block is tall and narrow (h large, w small) the block will be easier to tip (0tip is small). It is now not difficult to see why the automotive industry defines a safety factor describing how easily a vehicle will rollover as (roughly) vehicle width / vehicle height. The larger this safety factor is, the more resistant the vehicle is to rolling: Short and wide vehicles can take curves at high speeds without rolling, while tall and narrow vehicles cannot. While the torque responsible for tipping a vehicle going around a curve is different than in the case of the block on the incline, the principles involving torques that stabilize and de-stabilize the vehicle to rotation are the same. Table 1 - Tipping Angle Data for a Board on a Incline in Different Orientations trial Otip (°) w/h orientation 1 69 2 88 3 21 4 Your job: (a) Calculate the value of w/h for each of the trials in Table 1. (b) Match each of the trials with one of the orientations of the board shown below. (c) Use geometry/trigonometry to verify equation (1). A В D
Transcribed Image Text:Now consider the figure shown below. N CG -A tip In the above figure the block is just on the verge of tipping: W and N act through point A and thus exert zero torque about point A. The incline angle, Otip, is the incline angle beyond which the block will tip, since increasing the angle beyond Otip will move the CG beyond where there is a point of support below it, as in the previous figure. It is not difficult to show, using some geometry and trigonometry, that Otip is given by Orip = tan' (w / h) (1) Equation (1) agrees with our intuition: If the block is short and wide (h small, w large) the block will be more difficult to tip (Otip is large) and if the block is tall and narrow (h large, w small) the block will be easier to tip (0tip is small). It is now not difficult to see why the automotive industry defines a safety factor describing how easily a vehicle will rollover as (roughly) vehicle width / vehicle height. The larger this safety factor is, the more resistant the vehicle is to rolling: Short and wide vehicles can take curves at high speeds without rolling, while tall and narrow vehicles cannot. While the torque responsible for tipping a vehicle going around a curve is different than in the case of the block on the incline, the principles involving torques that stabilize and de-stabilize the vehicle to rotation are the same. Table 1 - Tipping Angle Data for a Board on a Incline in Different Orientations trial Otip (°) w/h orientation 1 69 2 88 3 21 4 Your job: (a) Calculate the value of w/h for each of the trials in Table 1. (b) Match each of the trials with one of the orientations of the board shown below. (c) Use geometry/trigonometry to verify equation (1). A В D
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