Shown above are six situations where vertically oriented circular disks have str

Question

Shown above are six situations where vertically oriented circular disks have strings wrapped around and attached to them. The other ends of the strings are attached to hanging masses. The radii of the disks and the hanging masses all vary and are given below.

Please note: the drawings are not to scale!

The disks, which are assumed to be weightless, are fixed and are not free to rotate.

List them in order of increasing torque exerted on the disk (magnitude only), from smallest to largest. (If B is smallest, then A, C, D, and finally E is largest, enter BACDE ) (Note: if of equal magnitude, then enter in the order listed)

A) M = 2.4 kg . . . . . . R = 54 cm
B) M = 2.5 kg . . . . . . R = 50 cm
C) M = 3 kg . . . . . . R = 12 cm
D) M = 2.6 kg . . . . . . R = 58 cm
E) M = 0.9 kg . . . . . . R = 18 cm
F) M = 1.3 kg . . . . . . R = 54 cm

Explanation / Answer

given,

mass and radius in differenct cases

A) M = 2.4 kg . . . . . . R = 54 cm
B) M = 2.5 kg . . . . . . R = 50 cm
C) M = 3 kg . . . . . . R = 12 cm
D) M = 2.6 kg . . . . . . R = 58 cm
E) M = 0.9 kg . . . . . . R = 18 cm
F) M = 1.3 kg . . . . . . R = 54 cm

torque = weight * radius

torque for cases

a) t_a = 2.4 * 9.8 * 0.54

t_a = 12.7 Nm

b) t_b = 2.5 * 9.8 * 0.50

t_b = 12.25 Nm

c) t_c = 3 * 9.8 * 0.12

t_c = 3.528 Nm

d) t_d = 2.6 * 9.8 * 0.58

t_d = 14.7784 Nm

e) t_e = 0.9 * 9.8 * 0.18

t_e = 1.5876 Nm

f) t_f = 1.3 * 9.8 * 0.54

t_f = 6.8796 Nm

torque from smallest to largest

t_e < t_c < t_f < t_b < t_a < t_d

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