Question

A roller coaster is passing through the very bottom of a semicircular section of track. (a) The FBD at right shows the forces acting on the cart at the bottom of the track, but the vectors are not necessarily drawn to scale. Which of the two forces must be larger? Explain in 1 - 2 sentences without equations or math, using what you know about circular motion and N2L. (b) The magnitude of the normal force acting on the coaster is 21 kN = 2.1 times 10^4 N, and the coaster's mass is 840 kg Starting from N2L and the FBD, calculate the coaster's acceleration at the bottom of the track. (c) Given that the radius of this section of track is 35 m, calculate the coaster's speed at this instant. (d) Suppose on the next pass the coaster crosses the bottom of the track at a lower speed than you found above. How would that affect the magnitudes of the following forces at that instant, compared to their current values?

Answer 1

If the rollercaster at the lowest position of the vertical circle, weight of the object(%) vertically downwards, normal reaction (%) towords the center.The difference between normal reaction and weight is equal to centripetal force..Therefore, Fyis larger than Fa. bNet force at bottom of the circle is (2.1x10 N)-(840kg) (98m/s2) (840kg)a Solve for accelerati on at bottom of the circle is, a 15.2m/s2 (c) Centripetal aceel erati on is, 152m/s) (35m) = 23 m/s (d) At lower speed.Fo (remains same).Fr (smaller) and Fu, (smaller)