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3 atempts left Check my work You take a homemade \"accelerometer\" to an amuseme

ID: 1865331 • Letter: 3

Question

3 atempts left Check my work You take a homemade "accelerometer" to an amusement park. This accelerometer consists of a meta nut attached to a string and connected to a protractor, as shown in the figure. While riding a roller coaster thatis moving at a uniform speed around a circular path, you hold up the accelerometer and notice that the string is making an angle of 55° with respect to the vertical with the nut pointing away from the center of the circle, as shown. 55° Center of roller coaster's circular path (a) What is the radial acceleration of the roller coaster? m/s2 (b) What is your radial acceleration expressed as a multiple of g? (e) If the roller coaster track is turning in a radius of 65.4 m, how fast are you moving? m/s

Explanation / Answer

(A).

look at free body diagram of metal nut, let T is string tension.

(SUMMATION)V = 0

T cos (th) = m g ...............(1)

(SUMMATION)H = m a

T sin (th) = m a......................(2)

eqn (2) divided by eqn (1)

a/g = tan (th)

a = g tan (th) = 9.81 tan 55° = 14.01 m/s²

(B).

a = g tan (th) = a = g tan 55° = 1.428 g

(C).

a = v²/R = g tan (th)

v²/65.4 = (9.81) tan 55°

v = 30.27 m/s