if a force of 100n stretches a spring by 0.1cm, find the work done in stretching the spring 0.3, if the elastic limit is not exceeded
To find the work done in stretching the spring by 0.3 cm, we first need to determine the spring constant. The spring constant (k) relates the force applied to the extension of the spring.
We can use Hooke's Law to calculate the spring constant:
F = k * x
where:
F is the force applied (in newtons),
k is the spring constant (in N/m),
x is the extension of the spring (in meters).
Given that a force of 100 N stretches the spring by 0.1 cm (or 0.001 m),
100 N = k * 0.001 m
k = 100 N / 0.001 m
k = 100,000 N/m
Now that we know the spring constant, we can calculate the work done to stretch the spring by 0.3 cm (or 0.003 m).
The work done on a spring is given by the equation:
W = (1/2) * k * x^2
W = (1/2) * 100,000 N/m * (0.003 m)^2
W = (1/2) * 100,000 N/m * 0.000009 m^2
W = (0.000009 N/m) * 100,000
W = 9 N*m or 9 joules
Therefore, the work done in stretching the spring by 0.3 cm (or 0.003 m), without exceeding the elastic limit, is 9 joules.