(The Drop of Doom) An amusement park ride that used to be lo
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(The Drop of Doom) An amusement park ride that used to be located at the West Edmonton Mall in Alberta, Canada, gives th
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(The Drop of Doom) An amusement park ride that used to be located at the West Edmonton Mall in Alberta, Canada, gives thrill seekers a taste of free-fall. It consists of a car moving along a track consisting of straight vertical and horizontal sections joined by a smooth curve. The car drops from the top and falls vertically under gravity for 10 ? 2 p2 7:2 m before entering the curved section at B. (See Figure 11.31.) It falls another 2 p2 2:8 m as it whips around the curve and into the horizontal section DE at ground level, where brakes are applied to stop it. (Thus, the total vertical drop from A to D or E is 10 m, a figure, like the others in this problem, chosen for mathematical convenience rather than engineering precision.) For purposes of this problem it is helpful to take the coordinate axes at a 45? angle to the vertical, so that the two straight sections of the track lie along the graph y D jxj. The curved section then goes from .?2; 2/ to .2; 2/ and can be taken to be symmetric about the y-axis. With this coordinate system, the gravitational acceleration is in the direction of i ? j.(a) Find a fourth-degree polynomial whose graph can be used to link the two straight sections of track without producing discontinuous accelerations for the falling car. (Why is fourth degree adequate?) (b) Ignoring friction and air resistance, how fast is the car moving when it enters the curve at B? at the midpoint C of the curve? and when it leaves the curve at D?(c) Find the magnitude of the normal acceleration and of the total acceleration of the car as it passes through C.
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