1/ A 0.462-m-long guitar string, of cross-sectional area 1.35 × 10 -6 m 2 ,

Question

1/ A 0.462-m-long guitar string, of cross-sectional area 1.35 × 10-6 m2, has Young's modulus Y = 1.87 × 109 N/m2. By how much must you stretch the string to obtain a tension of 15.7 N?

2/An anchor, made of cast iron of bulk modulus 66.0 × 109 Pa and of volume 0.268 m3, is lowered over the side of the ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.62 × 106 Pa. Find the change in the volume of the anchor.

3/The upper surface of a cube of gelatin, 5.69 cm on a side, is displaced 0.639 cm by a tangential force. If the shear modulus of the gelatin is 948 Pa, what is the magnitude of the tangential force?

4/A body is suspended vertically from an ideal spring of spring constant 3.17 N/m. The spring is initially in its relaxed position. The body is then released and oscillates about its equilibrium position. The motion is described by

y = (4.36 cm) sin [(0.772 rad/s)t]
What is the maximum kinetic energy of the body?

5/A clock has a pendulum that performs one full swing every 1.02 s (back and forth). The object at the end of the pendulum weighs 11.6 N. What is the length of the pendulum?

6/When the tension in a cord is 77.3 N, the wave speed is 135 m/s. What is the linear mass density of the cord?

7/Write an equation for a sine wave with amplitude 0.123 m, wavelength 0.221 m, and wave speed 6.07 m/s traveling in the -x-direction. y(x,t) = (a m)sin[( b s-1)t + (c m-1)x] where

a =

b =

c =

Explanation / Answer

1) Y = F*L/(A*e)=> e = F *L/ (Y*A) =Â 2.9 mm = 29 cm

2) bulk moulus = delta P*V / delta V===> delta V = delta p *V / B = 1.62*10^6*0.268/ 66*10^9 = 0.0.0066 *10^-3 m3

3) shear modulus = F*L/ (L^2*x) = F/ Lx ===> F = 948*.0569*0.00639 = 0.344684 N

4) KE max = 0.5* K*A^2 = 0.5*3.17*.0436^2 =Â 0.003013 J

5) T = 2*pi*sqrt(l / g) => l = 0.258 m

6) v = sqrt(T/u) => u = T/ V^2 = 0.004241 Kg /m

7) y(x,t) = (0.123 m)sin[(172.48 s-1)t + (28.41)x]

W = 2*pi*v/ lambda = 172.48 rad/s K = W/ v = 28.415

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