Steel will rapture if subjected to a shear stress of more that about 4.2 * 10 8 N/m2. What sideward
force is necessary to shear a steel bolt 1 cm in diameter?
To find the sideward force necessary to shear a steel bolt, we need to use the formula for shear stress, which is given by:
Shear Stress = Force / Area
Given:
Shear Stress = 4.2 * 10^8 N/m^2
Diameter of bolt = 1 cm
First, we need to calculate the area of the bolt. The formula for the area of a circle is:
Area = π * (radius)^2
Since the diameter is given, we need to divide it by 2 to get the radius:
Radius = Diameter / 2 = 1 cm / 2 = 0.5 cm
Next, we convert the radius from centimeters to meters:
Radius = 0.5 cm * (1 m / 100 cm) = 0.005 m
Now we can calculate the area of the bolt:
Area = π * (0.005 m)^2
Now, we substitute the given values into the equation for shear stress and solve for force:
4.2 * 10^8 N/m^2 = Force / (π * (0.005 m)^2)
To solve for force, we multiply both sides of the equation by the area:
Force = (4.2 * 10^8 N/m^2) * π * (0.005 m)^2
Calculating this expression will give us the sideward force necessary to shear the steel bolt with a diameter of 1 cm.
To determine the sideward force required to shear a steel bolt, we need to use the formula for shear stress:
Shear stress = Force / Area
Given that the shear stress threshold for steel is 4.2 * 10^8 N/m^2 and the bolt has a diameter of 1 cm, we can find the area of the bolt as follows:
Area = π * (diameter/2)^2
Substituting the values:
Area = π * (1 cm / 2)^2 = π * (0.5 cm)^2 = π * 0.25 cm^2
Now, we can rearrange the equation for shear stress to solve for the force:
Force = Shear stress * Area
Substituting the values:
Force = (4.2 * 10^8 N/m^2) * (π * 0.25 cm^2)
To find the sideward force, we need to convert the area from cm^2 to m^2, as the shear stress is given in N/m^2:
1 cm^2 = 0.0001 m^2
Substituting the conversion:
Force = (4.2 * 10^8 N/m^2) * (π * 0.25 * 0.0001 m^2)
Now we can calculate the force:
Force = (4.2 * 10^8 N/m^2) * (π * 0.25 * 0.0001 m^2)
After evaluating this expression, we can determine the sideward force needed to shear the steel bolt.
R = 0.01/2 =0.005 meters radius
A = pi R^2 = 3.14 * (0.005)^2 = 7.85 * 10^-5 m^2
F/ (7.85*10^-5) = 4.2 * 10^8
F = 33 *10^3 = 33,000 Newtons