1.A 3.0-kg stone is tied to a 0.60-m long string and swung around a circle at a

Question

1.A 3.0-kg stone is tied to a 0.60-m long string and swung around a circle at a constant angular
velocity of 25 rad/s. The net torque on the stone about the center of the circle is:

2.A certain wire stretches 0.70 cm when outward forces with magnitude F are applied to each end. The same forces are applied to a wire of the same material but with four times the diameter and five times the length. The second wire stretches in cm:

3.A cube with edges exactly 2 cm long is made of material with a bulk modulus of 3.5 x 109 N/m2. When it is subjected to a pressure of 3.0 x 105 Pa its volume in cm3 is:

4.A shearing force of 75 N is applied to an aluminum rod with a length of 10 m, a cross-sectional area of 1.0 x 10-5 m2, and a shear modulus of 25 x 109 N/m2. As a result the rod is sheared through a distance in mm of:

Explanation / Answer

1. torque = I alpha

w = constant so alpha = 0

torque = 0

2. (F/A)(L / deltaL) = Y = constant

(F / A)(L / 0.70) = (F / 16 A) (5 L / deltaL)

deltaL = 0.70 x 5 / 16 = 0.22 cm

3. V = 0.02^3

K = - V deltaP / deltaV

3.5 x 10^9 = - (0.02^3) (3 x 10^5) / deltaV

deltaV = - 6.86 x 10^-10 m^3  

V = (0.02^3) - (6.86 x 10^-10)

V = 7.99931 x 10^-6 m^3 = 7.99931 cm^3

4. (75) / (1 x 10^-5) = (25 x 10^9) (deltaL)/10

deltaL = 3 x 10^-3 m = 3 mm

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