Which of the following statements is true?
a. The original length of the spring(when no weight is attached) is 4.5 cm.
b. The original length of the spring(when no weight is attached) is 5 cm.
c. The length of the spring will be 13.5 cm when a weight of 6 kg is attached.
d. The length of the spring will be 12 cm when a weight of 5 kg is attached.
By the Hooke's Law
F=−kΔxLet x0= the original length of the spring(when no weight is attached).
We have
m1g=k(x1−x0)m2⋅g=k(x2−x0)Then
m1gm2g=k(x1−x0)k(x2−x0)m2(x1−x0)=m1(x1−x0)x0=m2−m1m2x1−m1x2x0=3 kg−1 kg3 kg(0.06 m)−1 kg(0.09 m)=0.045 mx0=4.5 cmk=0.06 m−0.045 m1 kg⋅9.81m/s2=654N/mx=kmg−x0m3=6 kg
x3=654N/m6 kg⋅9.81 m/s2+0.045 m=0.135 mx3=13.5 cmm4=5 kg
x4=654N/m5 kg⋅9.81 m/s2+0.045 m=0.12 mx4=12 cma. The statement is True.
b. The statement is False.
c. The statement is True.
d. The statement is True
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