Please show step by step for each! Thank You! 1) a massless spring has a spring

Question

Please show step by step for each! Thank You!

1) a massless spring has a spring constant of 8 N/m. how much mass should you add to the end of the spring constant in order to stretch the spring vertically by 1m?

Choice Options: 8.00 kg, 0.82, kg, 78.40 kg or 24.00 kg

2) what is the absolute pressure at the bottom of a lake, which is 754 ft. deep?

Choice Options: 0.15 MPa, 0.27 MPa, 7.01 M Pa or 2.35 MPa

3) the position of the object moving with simple harmonic motion is given by the equation, x=3cos(2piT), where x is in meters and t is in seconds. what is the period of the oscillating system?

Choice Options: 1.00 s, 2.00 s, 6.28 s, or 0.50 s

Explanation / Answer

1.

Using force balance:

Fg = Fs

m*g = k*d

m = k*d/g = 8*1/9.81 = 0.815 kg = 0.82 kg

2.

Absolute pressure is given by:

P = Patm + rho*g*h

rho = 1000 kg/m^3

h = 754 ft = 229.82 m

P = 1.013*10^5 + 1000*9.81*229.82

P = 2.35*10^6 Pa = 2.35 MPa

3.

T = 2*pi/w

In given equation, w = 2*pi

So,

T = 2*pi/(2*pi) = 1.00 sec

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