A hole 3cm in diameter is to be punched out of a steel plate 8cm thick. The shear stress of the material is 670GPa. What load is required on the punch?

First find the area:
A = pi*d^2/ 2
= 3.1416 * 3cm^2/ 2
= 3.1416 * 9/ 2
= 28.2744/ 2
= 7.0686cm

Stress = 670GPa
Second, covert 679Gpa to cm.
670Gpa = 6.7e+11N/m^2
= 67000000N/cm

Stress = Load/ Area

Force = Stress * Area
= 67000000 * 7.0686
= 4,735,962.00GN

I found this a little confusing. I could use a little help solving the question. Thank you.

Do not forget to multiply by 10^-4 when converting cm² to m²

Here we are talking about shear stress, which is dependent on the thickness and the circumference of the hole, not the area.

Surface area which resists shear force is similar to the lateral surface area of a cylinder:
As= πd *thickness
=π*3 cm * 8 cm
=24π cm²
=0.0024 m²

Shear strength, τu = 670 mPa

Load required
=As*τu
=0.0024*670*10^6 N
=1.608*10^6 N

To solve this question, you need to use the formula for stress, which is stress = force/area.

First, you need to find the area of the hole. You can use the formula for the area of a circle, which is A = πr^2. In this case, the diameter of the hole is given as 3cm, so the radius (r) would be half of the diameter, which is 1.5cm. Plugging these values into the area formula, you get A = π(1.5cm)^2 = 7.0686cm^2.

Next, you need to convert the shear stress from GPa to N/cm^2. The given shear stress is 670 GPa. To convert it to N/cm^2, you need to multiply it by 10^9 (since 1 GPa = 10^9 N/m^2) and then divide by 100 (since 1 m^2 = 10,000 cm^2). So, 670 GPa = 670,000,000,000 N/m^2 = 670,000,000 N/cm^2.

Now, you can use the stress formula to find the force required. Rearranging the formula, you get force = stress * area. Plugging in the values, force = 670,000,000 * 7.0686 = 4,735,962,000 N.

Therefore, the load required on the punch is 4,735,962,000 N.