Question
A spring 20cm long is stress to a 25cm by a load of 50n.what will be it new length when stress by 80n assuming that the elastic limit is not exceeded.
Answers
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We can use the formula for stress and strain to solve this problem:
stress = force / area
strain = change in length / original length
Since the spring is stretched, we can assume that the area is constant. Therefore, we can use the stress to find the strain:
strain = stress / modulus of elasticity
where the modulus of elasticity is a constant that depends on the material of the spring.
Let's assume that the modulus of elasticity for this spring is 20 N/cm². Then, we can calculate the strain caused by the first load of 50 N:
strain = 50 N / (20 N/cm²) = 2.5 cm/cm
This means that the spring increased its length by 2.5 cm for every 1 cm of its original length. Therefore, its new length under a load of 80 N would be:
change in length = strain * original length * force
change in length = (2.5 cm/cm) * (20 cm) * (80 N)
change in length = 400 cm
new length = original length + change in length
new length = 20 cm + 400 cm
new length = 420 cm
Therefore, the new length of the spring under a load of 80 N would be 420 cm, assuming that the elastic limit is not exceeded.
stress = force / area
strain = change in length / original length
Since the spring is stretched, we can assume that the area is constant. Therefore, we can use the stress to find the strain:
strain = stress / modulus of elasticity
where the modulus of elasticity is a constant that depends on the material of the spring.
Let's assume that the modulus of elasticity for this spring is 20 N/cm². Then, we can calculate the strain caused by the first load of 50 N:
strain = 50 N / (20 N/cm²) = 2.5 cm/cm
This means that the spring increased its length by 2.5 cm for every 1 cm of its original length. Therefore, its new length under a load of 80 N would be:
change in length = strain * original length * force
change in length = (2.5 cm/cm) * (20 cm) * (80 N)
change in length = 400 cm
new length = original length + change in length
new length = 20 cm + 400 cm
new length = 420 cm
Therefore, the new length of the spring under a load of 80 N would be 420 cm, assuming that the elastic limit is not exceeded.