A spring 20cm long is stretched to 25cm by a load of 59N. What will be its length when stretched by 100N assuming that the elastic limit is reached?
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To answer this question, we can use Hooke's Law, which states that the force applied to a spring is directly proportional to the extension or compression of the spring, as long as the elastic limit is not exceeded. Mathematically, Hooke's Law is expressed as:
F = k * x
Where:
F is the force applied to the spring
k is the spring constant, which represents the stiffness of the spring
x is the extension or compression of the spring
In this case, we know the initial length of the spring (20cm), the new length when stretched by a load of 59N (25cm), and the force applied to find the new length (100N). We need to find the unknown length when stretched by 100N.
First, we need to calculate the spring constant (k) using the initial length and the load of 59N:
F = k * x
59N = k * (25cm - 20cm)
59N = k * 5cm
k = 59N / 5cm
k = 11.8 N/cm
Now that we know the spring constant (k), we can use it to calculate the length (x) when stretched by 100N:
F = k * x
100N = 11.8 N/cm * x
x = 100N / 11.8 N/cm
x ≈ 8.47 cm
Therefore, the length of the spring when stretched by 100N will be approximately 8.47 cm.