DynamicsofUniformCircularMotion勻速圓周運(yùn)動(dòng)的動(dòng)力學(xué)

1、1會(huì)計(jì)學(xué)DynamicsofUniformCircularMotion勻勻速圓周運(yùn)動(dòng)的動(dòng)力學(xué)速圓周運(yùn)動(dòng)的動(dòng)力學(xué)d = 100mHow fast would the outer most part of the space station have to spin in order to have a centripetal acceleration of 9.8 m/s2 d = 100mA bobsled goes down a track, moving at a constant velocity throughout all three turns. At which turn wil

2、l there be the greatest centripetal acceleration?AB CD All the sameIf the bobsled moves at 35 m/s throughout the course and turn B has a radius of 20m and turn C is 50m how many Gs of acceleration is the sledder feeling through turns B & C ?F = mv2 rNote that v2/r = accelerationA 50 kg person an

3、d a 100 kg person ride the “Enterprise” at Valleyfair. The ride has a radius of 7 meters and takes 4 seconds per revolution. How much centripetal force does each person feel at point A & C?“Gondolas start out hanging from the ride, then go to a horizontal position by centrifugal force from the s

4、pinning ride, which then lifts to a vertical position turning riders upside down.” A CDBAt what point will a person feel the most centripetal force?ABCD E= all the sameA soapbox racer is making a turn on asphalt at 20 m/s. The coefficient of frictionstatic is .9. The radius of the turn is 40 m. Will

5、 the soapbox crash into the hay? Why or why not? When a car turns a corner, there is a centripetal force toward the center of the circle. The force that is being applied to the center of the circle is coming from static friction between the car and the ground. If the rubber on the car cannot handle

6、the centripetal force, the car will slide. Static Friction is keeping the car from slidingFc = FN = mv2/r mg = mv2/rV2 = mgr / m = grV = sqrt .9(9.8)(40) = 18.8 m/s max speed around the turn *this equation indicates that for a given speed, the centripetal force needed for a turn of radius r can be o

7、btained by banking the turn at an angle, independent of the mass of the vehicle.Tan = v 2 r gMr. Shaf hotA racetrack is designed with a 40o bank angle and a radius of 240 m at the ends. At what speed is the track designed for cars to make an ideal turn? V = sqrt (tan )rg = sqrt (tan 40)(240m)(9.8m/s

8、2)= 44.4 m/s40odmg140.5m d = 140.5 sin 50 = 183.4 mUsing the equation tan = v2 / rg we want to find the radius of the turn. Once we have the radius, well us trig to find d r = v2 / tan (g) = 342 / tan 40 (9.8) = 140.5 m 50o40od Fc = FN cos = mv2 / r if we can find the radius of the turn, we can find

9、 d using trig. Solving for r, r = mv2 since FN = mg/sin50, well substitute this in FN cos r = mv2 = v2 (sin50) = 342 (sin50) = 885 = 140.5m mgcos g cos 9.8(cos 500) 6.3 (sin50)FNFc =FN(Cos ) = mv2 / r50omg FN sin 50 mg = 0 (no vertical acceleration)50o140.5md = 140.5 sin 50 =183.4 mThe centripetal f

10、orce acting on satellites is gravity:Fc = G m1m2 = mv2 r2 rv = GME T = 2r3/2 r GMEHow many miles per hour is the earth orbiting the sun? (93,000,000 miles radius)(mass of sun = 2 x 1030)Synchronous satellites are satellites that orbit the earth with no movement relative to the earths surface. V = GM

11、E rV = GME rA = v2 / rIf an object is in freefall, the centripetal force is gravitational force (mg). mgmgIf an airplane does a parabolic downward turn to simulate artificial weightlessness, what would the radius of the turn have to be if the airplane flew the turn with a speed of 100 m/s (220 mi/hr)?d = 100mA bobsled goes down a track, moving at a constant velocity throughout all three turns. At which turn will there be the greatest centripetal acceleration?AB CD All the sameIf the bobsled moves at 35 m/s throughout the course and turn B has a radius of 20m and tu