A copper wire with a length 2.0m, cross sectional area 7.1x10^-6 m^2 and young's modulus 11x10^10 N/m^2 has a 200kg load hung on it. What is its increase the length? (g=9.8 m/s^2)
im not sure how to start this problem or what equation to use, can some one help me out with this problem.
5.0 mm
To solve this problem, we can use Hooke's Law, which states that the stress (force per unit area) on a material is directly proportional to the strain (change in length per unit length) it produces.
The formula for Hooke's Law is:
Stress = Young's modulus × Strain
In this case, the stress is the weight of the load (force) divided by the cross-sectional area of the wire, and the strain is the change in length of the wire divided by its original length.
Step 1: Calculate the stress:
Stress = Force / Area
= (mass × gravity) / Area
= (200 kg × 9.8 m/s²) / (7.1 × 10^-6 m²)
= 2.75 × 10^10 Pa
Step 2: Rearrange the formula for Hooke's Law to solve for strain:
Strain = Stress / Young's modulus
Step 3: Calculate the strain:
Strain = 2.75 × 10^10 Pa / (11 × 10^10 N/m²)
= 0.25
Step 4: Calculate the change in length:
Change in length = Strain × Original length
= 0.25 × 2.0 m
= 0.5 m
Therefore, the wire will increase in length by 0.5 meters when a 200 kg load is hung on it.
To solve this problem, we can use Hooke's Law, which states that the force exerted on a spring or elastic material is directly proportional to the displacement caused by the force. In mathematical form, Hooke's Law can be written as:
F = k * ΔL
Where:
F is the force applied,
k is the spring constant or Young's modulus,
ΔL is the change in length of the wire.
In this case, we are given the following values:
Length of the wire (original length) = 2.0 m
Cross-sectional area = 7.1 × 10^-6 m^2
Young's modulus = 11 × 10^10 N/m^2
Load = 200 kg
To find the increase in length (ΔL), we need to calculate the force applied (F). The force can be calculated using the formula:
F = m * g
Where:
m is the mass of the load,
g is the acceleration due to gravity (9.8 m/s^2).
Substituting the given values, we get:
F = 200 kg * 9.8 m/s^2
F ≈ 1960 N
Now, we can rearrange Hooke's Law equation and solve for ΔL:
ΔL = F / k
Substituting the values, we get:
ΔL = 1960 N / (11 × 10^10 N/m^2)
Calculating the value, we get:
ΔL ≈ 1.78 × 10^-8 m
Hence, the increase in length of the copper wire is approximately 1.78 × 10^-8 meters.