A force of 100 N is required to compress a spring by 0.01 m. Determine the force

Question

A force of 100 N is required to compress a spring by 0.01 m. Determine the force needed to compress the spring by 0.05 m. (A) 240 N (B) 10000 N (C) 50000 N (D) 500 N (E) 120 N A spring stretches by 0.01 m when a 5-kg object is suspended from its end. How much mass should be suspended to this spring so that its vibration frequency is f = 3 Hz? (A) 5.34 kg (B) 2.80 kg (C) 10.7 kg (D) 13.8 kg (E) 0.02 kg A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy. The gasoline burned in a 260-mile trip in a typical midsize car produces about 1.30 times 10^9 J of energy. How fast would a 16-kg flywheel with a radius of 0.32 m have to rotate to store this much energy? Give your answer in rev/min. (A) 538 rev/min (B) 0.01 times 10^5 rev/min (C) 2.70 times 10^5 rev/min (D) 10.8 times 10^5 rev/min (E) 5.40 times 10^5 rev/min

Explanation / Answer

problem 14:

spring force=spring constant*compression

for compression=0.01 m, spring force=100 N

==>spring constant=100/0.01=10^4 N/m

for compression of 0.05 m, spring force=10^4*0.05=500 N

so option D is correct.

problem 15:

spring constant=force/compression

=5*9.8/0.01=4900 N/m

frequency=(1/(2*pi))*sqrt(spring constant/mass)

==>3=(1/(2*pi))*sqrt(4900/mass)

==>mass=4900/(2*pi*3)^2=13.791 kg=13.8 kg

so option D is correct.

problem 16:

moment of inertia of the solid disk=0.5*m*r^2

where m=mass=16 kg

r=0.32 m

rotational kinetic energy=0.5*moment of inertia*angular speed^2

==>1.3*10^9=0.5*0.5*16*0.32^2*angular speed^2

==>angular speed=sqrt(1.3*10^9/(0.5*0.5*16*0.32^2))

=5.6337*10^4 rad/s

=4.3798*10^5 rev/min

hence option E is correct.

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