If the ultimate shear strength of steel is taken to be 2.00 109 Pa, what force is required to punch through a steel plate 1.60 cm thick? Assume the superhero's fist has cross-sectional area of 1.20 102 cm2 and is approximately circular. answer in Newtons
To find the force required to punch through a steel plate, we can use the formula for pressure:
Pressure = Force / Area
Given information:
Ultimate shear strength of steel (σ) = 2.00 * 10^9 Pa
Thickness of the steel plate (h) = 1.60 cm
Cross-sectional area of the superhero's fist (A) = 1.20 * 10^2 cm^2
First, convert the thickness of the steel plate to meters:
Thickness of the steel plate (h) = 1.60 cm = 1.60 * 10^-2 m
Convert the cross-sectional area of the fist to square meters:
Cross-sectional area of the superhero's fist (A) = 1.20 * 10^2 cm^2
Cross-sectional area of the superhero's fist (A) = 1.20 * 10^-4 m^2
Now, we can calculate the force required to punch through the steel plate using the pressure formula:
Pressure = Force / Area
Rearranging the formula:
Force = Pressure * Area
Substituting the given values:
Force = (2.00 * 10^9 Pa) * (1.20 * 10^-4 m^2)
Calculating the force:
Force = (2.00 * 10^9 * 1.20 * 10^-4) N
Force = 2.40 * 10^5 N
Therefore, the force required to punch through the steel plate is 2.40 * 10^5 Newtons.
To find the force required to punch through the steel plate, we need to calculate the pressure exerted by the superhero's fist on the steel plate and then multiply it by the cross-sectional area of the fist.
Let's break down the steps to find the force:
Step 1: Convert the thickness of the steel plate from centimeters to meters.
Given: Thickness of steel plate (h) = 1.60 cm
Conversion: 1 cm = 0.01 m
Therefore, the thickness in meters (h) = 1.60 cm × 0.01 m/cm
Step 2: Calculate the pressure exerted on the steel plate.
The pressure (P) is given by the formula:
P = F/A
where P is pressure, F is force, and A is the cross-sectional area of the fist.
Step 3: Convert the cross-sectional area of the fist from square centimeters to square meters.
Given: Cross-sectional area of the fist (A) = 1.20 × 10^2 cm^2
Conversion: 1 cm^2 = (0.01 m)^2
Therefore, the cross-sectional area in square meters (A) = 1.20 × 10^2 cm^2 × (0.01 m/cm)^2
Step 4: Substitute the given values into the equation for pressure.
P = F/A
P = (2.00 × 10^9 Pa) (since the ultimate shear strength is the maximum pressure the steel can withstand)
Step 5: Solve for the force (F).
F = P × A
F = (2.00 × 10^9 Pa) × (1.20 × 10^2 cm^2 × (0.01 m/cm)^2)
Step 6: Simplify and convert the units to Newtons.
Make sure the units match up before multiplying:
1 kg/m^2 = 1 Pa
1 N = 1 kg × m/s^2
By solving the equation in Step 5 and confirming the units match up, you'll find the force required to punch through the steel plate in Newtons.