a).A 45.5 g mass is attached to a horizontal spring with a spring constant of 15

Question

a).A 45.5 g mass is attached to a horizontal spring with a spring constant of 15.3 N/m and released from rest with an amplitude of 35.9 cm.What is the velocity of the mass when it is halfway to the equilibrium position if the surface is frictionless?

Answer in units of m/s

b). If a 1-megaton nuclear weapon is exploded at ground level, the peak overpressure (that is, the pressure increase above normal atmospheric pressure) will be 0.2 atm at a distance of 6 km. What force due to such an explosion will be exerted on the side of a house with dimensions 2.55 m

Explanation / Answer

(a)
You use
1/2mv^2 + 1/2kx^2 = 1/2kA^2
given that x = 1/2 A
1/2mv^2 + 1/8kA^2 = 1/2kA^2
1/2mv^2 = 3/8 kA^2
mv^2 = 3/4 kA^2
0.0455 v^2 = 3/4 * 15.3 * (0.359)2
v^2 = 32.5
v = 5.7 m/s

(b)
Force, F = P*A
P = 0.2 atm = 0.2 * 101325 Pa = 20265 Pa
A = 2.55 x 11.6 = 29.58 m2
F = 20265 * 29.58
F = 5.99 x 105 N

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