What hanging mass will stretch a 1.6 meter long, 0.66cm diameter steel wire by 1.4cm.?
Need answer in kg. ( this is all that is in the question , no other hints given).
look up the modulus of elasticity of steel, about 220GPa.
Force= 220GPa*area*deltaL/L
mass*g=force
so mass= 220GPa*PI(.0033)^2*.14/1.6*9.8
check that.
To find the hanging mass that will stretch the steel wire by a given length, we can use Hooke's law, which states that the force exerted by a spring is directly proportional to its extension (displacement) from its equilibrium position.
The formula for Hooke's law is: F = k * x,
where F is the force applied on the spring, k is the spring constant (also known as the stiffness or spring rate), and x is the displacement of the spring from its equilibrium position.
In this case, the steel wire can be approximated as a spring, and the given displacement is 1.4 cm. The length of the wire is 1.6 meters, and the diameter is 0.66 cm.
Step 1: Calculate the radius
The diameter (0.66 cm) is given, so we need to calculate the radius by dividing it by 2:
radius = diameter / 2
radius = 0.66 cm / 2
radius = 0.33 cm
Step 2: Convert the radius to meters
To maintain consistency with the length of the wire (1.6 meters), we need to convert the radius from centimeters to meters:
radius = 0.33 cm * (1 meter / 100 centimeters)
radius = 0.0033 meters
Step 3: Calculate the cross-sectional area of the wire
The cross-sectional area of a wire is given by the formula: A = π * r^2,
where A is the cross-sectional area and r is the radius.
cross-sectional area = π * r^2
cross-sectional area = 3.14 * (0.0033 meters)^2
Step 4: Calculate the spring constant (k)
The spring constant depends on the material and geometry of the wire. In this case, we can assume it is a linear relation:
k = (spring force) / (spring extension)
k = (hanging mass) * g / x,
where g is the acceleration due to gravity (approximately 9.8 m/s^2).
Step 5: Rearrange the formula to solve for hanging mass (m)
m = (k * x) / g,
where m is the hanging mass.
Now we can substitute the given values into the equation:
m = (k * x) / g
m = (k * 0.014 meters) / 9.8 m/s^2
To calculate the spring constant (k), we need to know the type of steel and its Young's modulus. Without specific details, we won't be able to provide an accurate answer for the hanging mass in kg.