Question
A force of 1.8 N extends a wire by 0.4 cm , what force will extend the wire by 1.25 cm if the elastic limit is not exceeded
Answers
GPT 3.5
To solve this problem, we can use Hooke's Law, which states that the force required to extend or compress a spring is directly proportional to the amount of stretch or compression. The formula for Hooke's Law is:
F = k * x
Where:
F = force applied (unknown)
k = spring constant (unknown)
x = amount of stretch (1.25 cm = 0.0125 m)
We can first find the spring constant, k, using the given information:
1.8 N = k * 0.004 m
k = 1.8 N / 0.004 m
k = 450 N/m
Now, we can use the spring constant to find the force (F) required to extend the wire by 1.25 cm:
F = 450 N/m * 0.0125 m
F = 5.625 N
Therefore, a force of 5.625 N will extend the wire by 1.25 cm without exceeding the elastic limit.
F = k * x
Where:
F = force applied (unknown)
k = spring constant (unknown)
x = amount of stretch (1.25 cm = 0.0125 m)
We can first find the spring constant, k, using the given information:
1.8 N = k * 0.004 m
k = 1.8 N / 0.004 m
k = 450 N/m
Now, we can use the spring constant to find the force (F) required to extend the wire by 1.25 cm:
F = 450 N/m * 0.0125 m
F = 5.625 N
Therefore, a force of 5.625 N will extend the wire by 1.25 cm without exceeding the elastic limit.