Answer:
2800 [MPa]
Explanation:
In fracture mechanics, whenever a crack has the shape of a hole, and the stress is perpendicular to the orientation of such, we can use a simple formula to calculate the maximum stress at the crack tip
Where is the magnitude of he maximum stress at the tip of the crack,
is the magnitude of the tensile stress,
is
the length of the internal crack, and
is the radius of curvature of the crack.
We have:
We replace:
We get:
Answer:
1.176
Explanation:
When the bullets impact the mass they become embedded on it, it is a plastic collision, therefore momentum is conserved.
v2 * (M + mb) = v1 * mb
Where
v1: muzzle velocity of the bullet
M: mass of the bob
mb: mass of the bullet
v2: mass of the bob with the bullet after being hit
v2 = v1 * mb / (M + mb)
Upon being impacted the bob will acquire speed v2, this implies a kinetic energy. The bob will then move and raise a height h. Upon acheiving the maximum height it will have a speed of zero. At that point all kinetic energy will be converted into potential energy.
Ek = 1/2 (M + mb) * v2^2
Ep = (M + mb) * g * h
Ek = Ep
1/2 (M + mb) * v2^2 = (M + mb) * g * h
1/2 * (v1 * mb / (M + mb))^2 = g * h
1/2 * v1^2 * mb^2 / (M + mb)^2 = g * h
v1^2 = g *h * (M+ mb)^2 / (1/2 * mb^2)
The height h that it reaches is related to the length L of the pendulum arm and the angle it forms with the vertical.
h = L * (1 - cos(a))
For the 9 mm:
For the 0.44 caliber:
The ratio is 460 / 391 = 1.176