What hanging mass will stretch a 2.2-m-long, 0.40 - diameter steel wire by 1.1 ?
What are the units of the 1.1 number?
You will need to look up Young's modulus for steel, E.
amount of stretch = Length*Stress/E
Stress = M g/(wire area)
Solve for M
To find the hanging mass that will stretch a steel wire by a certain length, we need to use Hooke's law, which states that the extension or elongation of an elastic material is directly proportional to the applied force. The formula for Hooke's law is:
F = k * ΔL
Where:
F is the force applied to the material,
k is the spring constant (also known as the stiffness constant), and
ΔL represents the change in length (stretch or compression) of the material.
In this case, the steel wire is being stretched by a hanging mass, so we need to find the force applied to the wire and then calculate the mass equivalent of that force.
The force applied to the steel wire is the weight of the hanging mass, which can be calculated using the formula:
F = m * g
Where:
F is the force applied to the wire,
m is the mass of the hanging mass, and
g is the acceleration due to gravity (approximately 9.8 m/s^2).
Since we are given the change in length (ΔL) and the original length of the wire, we can calculate the force applied to the wire using the formula:
F = k * ΔL
Now, we can substitute the formulas and values into the equation as follows:
m * g = k * ΔL
We want to find the mass (m) of the hanging mass, so we rearrange the equation:
m = (k * ΔL) / g
To find the spring constant (k) for the steel wire, we can use the formula:
k = (4 * L * E) / (π * d^2)
Where:
L is the length of the wire,
E is the Young's modulus of the material, and
d is the diameter of the wire.
The Young's modulus for steel is approximately 200 GPa (GigaPascals), and we are given the length (L) and diameter (d) of the wire.
Now we can plug in the values and solve for the hanging mass (m).