We can use Hooke's Law to solve this problem. Hooke's Law states that the force exerted by a spring is directly proportional to the displacement or change in length of the spring. Mathematically, it can be represented as:
F = kx
Where:
F = force applied to the spring (in Newtons)
k = spring constant (in Newtons per meter)
x = change in length of the spring (in meters)
We are given that the spring is stretched from 30cm (0.3m) to 35cm (0.35m) by a load of 50N. Let's use these values to find the spring constant (k):
50N = k(0.35m - 0.3m)
50N = k(0.05m)
Now, solve for k:
k = 50N / 0.05m
k = 1000 N/m
Now, we can use the spring constant to find the change in length (x) when a force of 100N is applied:
100N = (1000 N/m) x
x = 100N / 1000 N/m
x = 0.1m
Finally, we can calculate the final length of the spring when stretched by 100N:
New length = original length + change in length
New length = 0.35m + 0.1m
New length = 0.45m
Therefore, the spring will be 45cm long when stretched by 100N.
A spring 30cm long is stretched to 35cm by a load of 50N.What will be its length when stretched by 100N assuming that the elastic limit is not reached?
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