Safari File Edit View History Bookmarks W (b) Find the magnitude of the tension

Question

Safari File Edit View History Bookmarks W (b) Find the magnitude of the tension in the monkey's arm. Additional Materials Section 5.3 6. 0-4 points CJ10 5P043 Suppose, for example, that the track has a radius of 2.8 m and that the driver goes past point 1 at the bottom with a speed of 13 m/s What speed must she have at point 3, so that the normal force at the top has the same magnitude as it did at the bottom? For the normal force in the figure to have the same magnitude at all points on the vertical track, the stunt driver must adjust the speed to be different at different points m/s

Explanation / Answer

Given,

V1 = 13 m/s ; r = 2.8

At point 3,

Fc = Fn + mg = m V3^2/r (1)

at point 1,

Fc = Fn - mg = m V1^2/r (2)

(1) - (2)

2 mg = m V3^2/r - m V1^2/r

V3^2 = 2 gr + V1^2

V3 = sqrt (2 gr + V1^2) = sqrt (2 x 9.81 x 2.8 + 13^2) = 14.96 m/s

Hence, V3 = 14.96 m/s (=15 m/s aprox)

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