A force of 12 kg stretches a spring 3 cm. How far will the spring stretch given a force of 30 kg?

Question

A force of 12 kg stretches a spring 3 cm. How far will the spring stretch given a force of 30 kg??  
A. 6 cm  
B. 7.5 cm  
C. 9 cm  
D. 10.5 cm

Accepted Answer

Correct Answer: (B)7.5 cm. 
Rationale: The spring will stretch 7.5 cm when a force of 30 kg is applied.The stretching of a spring under an applied force follows Hooke’s law, which states that the extension of a spring is directly proportional to the applied force, provided the elastic limit is not exceeded. This relationship is expressed as:Force = spring constant × extensionwhere F is the force, x is the extension, and k is the spring constant.From the given information, a force of 12 kg produces an extension of 3 cm. This allows the spring constant to be determined and then used to calculate the new extension under a larger force.A) 6 cmThis value would correspond to doubling the original extension from 3 cm to 6 cm. However, doubling the extension would require doubling the force from 12 kg to 24 kg. Since the applied force is 30 kg, not 24 kg, this option underestimates the stretch.B) 7.5 cmUsing Hooke’s law, the spring constant is calculated as:spring constant = force ÷ extensionspring constant = 12 kg ÷ 3 cmspring constant = 4 kg per cmApplying a force of 30 kg gives:extension = force ÷ spring constantextension = 30 kg ÷ 4 kg per cmextension = 7.5 cmThis result follows the correct proportional relationship between force and extension.C) 9 cmAn extension of 9 cm would represent three times the original stretch of 3 cm. That amount of stretching would require a force of 36 kg, not 30 kg. This option overestimates the extension.D) 10.5 cmThis value appears to result from adding the original 3 cm extension to 7.5 cm, rather than calculating the total extension directly from the applied force. Hooke’s law requires proportional scaling, not additive reasoning, making this approach incorrect.ConclusionBecause extension is directly proportional to force under Hooke’s law, calculating the spring constant from the initial data and applying it to the new force shows that the spring stretches 7.5 cm.

A force of 12 kg stretches a spring 3 cm. How far will the spring stretch given a force of 30 kg?

A
6 cm

B
7.5 cm

C
9 cm

D
10.5 cm

The spring will stretch 7.5 cm when a force of 30 kg is applied.

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A force of 12 kg stretches a spring 3 cm. How far will the spring stretch given a force of 30 kg?

A 6 cm B 7.5 cm C 9 cm D 10.5 cm

The spring will stretch 7.5 cm when a force of 30 kg is applied.

Topic Flashcards

Mini Quiz

Related Questions

A
6 cm

B
7.5 cm

C
9 cm

D
10.5 cm