Question

Problem 3. (30 points) yo Steep safety ramps are built besides mountain highways to enable vehicles with defective brakes to stop. A 10 ton truck enters a 15° ramp at high speed vo 100 ft/s and travels for 8 seconds before its speed is reduced to 30 ft/s. assuming constant deceleration, RAIL INES vo 15 (a) the magnitude of the braking force, (b) the additional time needed for the truck to stop. Note: 1 ton = 2000 lb

Answer 1

liven: - Mass of treucle = loton Anelination of vamp with houizontal - 150 Initial speed of truck, vo 100ft/s After a seconds, speed of truck is reduced to soft's Debeleuation of fuucle is eenutant. Yo find :- as Magritude of the bushing touce by additional time needed for the truuck to step ay Magnitude of the braking force Asume that since, the given track is moving up the slope, the braking force (f) will act down the slope. first of all, let's draw the fuce-body diaguam of farces acting on the truck. Now, find the deceleration of truck wing the equation of veut at Here, rego v=30fts substituting these values in equation o trucks ma motion, mgain 154 simg cose song © Uz 100 coft's 3o = loo + 8a Pa = -40 as-8.75 8.75 ft/se

gjinisº) The truck needs additional 3.42 seconds to come to stop. wa V = 0 t=3.42 seconds. Consider the equilibuium of faces in the direction of motion of truck. ma-mgsins-fco Fama-mgsinsso f = mla- Fa doxalood (-8.75-6ll sin 15°)) malo ton, iton=2000) 10 ton = (lox2000 lb g= 32. 2 ft/sh f = mooto (-8.45 - 8.33) fa 20000 x (-17.00) fa - 842,600 pound force Negative sign shows that our the direction of braking fouce assumption seegadeding fosice will act in the direction of motion! Lorong The breaking b.) Additional time needed fare the trucke to stop. The truck will stop aften some time when the speed of truct is softls. This additional time is calculated equation the motion's using V = utat. L truck came to rest) u= 30ft/s -8.75ft/s? 0 = 50 -8.75t Hole, pubstituting these value o equations