A manufacturer wishes to produce crude benzene models for the chemistry department. The manufacturer plans to do this by punching regular hexagons out of steel. If the steel plate is 0.500 cm thick, What is the minimum shearing force needed to punch regular hexagons with sides of length 5.56 cm? ________N Note: Assume that if the shear stress in steel exceeds 4.0 x 10^8 N/M^2 the steel ruptures.
To find the minimum shearing force needed to punch regular hexagons out of the steel plate, we need to calculate the shearing stress on the steel.
The formula for shearing stress is:
Shearing stress = Shearing force / Area
The area of a regular hexagon can be calculated using the formula:
Area = (3 * √3 * s^2) / 2
Where s is the length of the side of the hexagon.
Given:
Thickness of the steel plate (d) = 0.500 cm = 0.005 m
Length of the side of the hexagon (s) = 5.56 cm = 0.0556 m
Maximum shearing stress for rupture (σ_max) = 4.0 x 10^8 N/m^2
First, we need to calculate the area of the hexagon:
Area = (3 * √3 * s^2) / 2
= (3 * √3 * (0.0556)^2) / 2
= 0.04502 m^2
Next, we can rearrange the formula for shearing stress to solve for the shearing force:
Shearing stress = Shearing force / Area
Rearranging,
Shearing force = Shearing stress * Area
Let's assume shearing stress to be the maximum allowed value (σ_max) in order to find the minimum shearing force:
Shearing force = σ_max * Area
= (4.0 x 10^8 N/m^2) * 0.04502 m^2
= 1.8008 x 10^7 N
Therefore, the minimum shearing force needed to punch regular hexagons with sides of length 5.56 cm from the steel plate is approximately 1.8008 x 10^7 N.
To determine the minimum shearing force needed to punch regular hexagons out of steel, we need to consider the shear stress and the area of the hexagon.
The formula for shear stress is given by:
Shear stress = Force / Area
We can rearrange the formula to solve for Force:
Force = Shear stress * Area
First, let's calculate the area of the hexagon. Since the hexagon is regular, we know that all sides are equal and all angles are 120 degrees.
To find the area of a regular hexagon, we can use the formula:
Area = (3 * sqrt(3) * side^2) / 2
Given that the side length of the hexagon is 5.56 cm, we can substitute this value into the formula to find the area:
Area = (3 * sqrt(3) * (5.56 cm)^2) / 2
Next, let's determine the shear stress. We know that the steel ruptures if the shear stress exceeds 4.0 x 10^8 N/m^2.
Now, we need to convert the thickness of the steel plate to meters, since the shear stress is given in N/m^2.
0.500 cm = 0.005 m (conversion factor: 1 cm = 0.01 m)
Finally, let's substitute these values into the formula to calculate the minimum shear force:
Force = Shear stress * Area
Force = (4.0 x 10^8 N/m^2) * (0.005 m) * [(3 * sqrt(3) * (5.56 cm)^2) / 2]
Now, we can simplify this expression to find the minimum shearing force needed in N.
Thanks a lot
F(min)/A = 4.0*10^8 N/m^2
A = 6*(0.0556)*(0.005) m^2
= 1.668*10^-3 m^2
is the load-bearing area.
Solve for F(min)