A force of 15N stretches a spring to a total length of 30cm. An additional force of 10N stretches the spring 5cm further. Find the natural length of the spr...
Question 1 Report
A force of 15N stretches a spring to a total length of 30cm. An additional force of 10N stretches the spring 5cm further. Find the natural length of the spring
Answer Details
We can use Hooke's Law, which states that the force exerted by a spring is proportional to its extension, to solve this problem. Let the natural length of the spring be x. When a force of 15N is applied, the spring is stretched by 30cm - x. Therefore, we have: 15N = k(30cm - x) where k is the spring constant. When an additional force of 10N is applied, the spring is stretched by an additional 5cm. Therefore, we have: 25N = k(35cm - x) Dividing the second equation by the first, we get: 25N/15N = (35cm - x)/(30cm - x) Simplifying this equation, we get: 5/3 = (35cm - x)/(30cm - x) Multiplying both sides by 30cm - x, we get: 5(30cm - x) = 3(35cm - x) 150cm - 5x = 105cm - 3x 2x = 45cm x = 22.5cm Therefore, the natural length of the spring is 22.5cm. Answer: 22.5cm.
Download The App On Google Playstore
Everything you need to excel in your exams
Personalized AI Learning Chat Assistant
200,000+ Exam Questions Across IGCSE, JAMB, WAEC & NECO
Over 3,900 Lesson Notes
Offline Support - Learn Anytime, Anywhere
Green Bridge Timetable
Literature Summaries & Potential Questions
Track Your Performance & Progress
In-depth Explanations for Comprehensive Learning