Answer:
a) F1 = 1999.8 N
, F2 = 4545 N
, F3 = 2778 N
, c) the cans do not collapse because the pressure is applied on both sides
Explanation:
Let's use the pressure equation
P = F / A
Suppose we have atmospheric pressure 1.01 10⁵ Pa
Let's calculate the area of the can that is a parallelepiped
Length L = 25 cm
width a = 18 cm
high h = 11 cm
Side area A = h a
A = 11 18
A1 = 198 10⁻⁴ m²
Lid area
A2 = L a
A2 = 25 18
A2 = 450 10⁻⁴ m²
Other side area
A3 = L h
A3 = 25 11
A3 = 275 10⁻⁴ m²
Now let's calculate the force on these sides
Side 1
F1 = P * A1
F1 = 1.01 10⁵ 198 10⁻⁴
F1 = 1999.8 N
Side 2
F2 = P A2
F2 = 1.01 10⁵ 450 10⁻⁴
F2 = 4545 N
Side 3
F3 P A3
F3 = 1.01 10⁵ 275 10⁻⁴
F3 = 2778 N
We see that the force is greater on side 2 which is where the can should collapse
b) To compare the previous forces we must use the concept of density, in general the cans are made of aluminum that has a density of 2700 kg / m3
d = m / V
m = d * V
V = L a h
V = 0.25 0.18 0.11
V = 0.00495 m3
m = 2700 0.00495
m = 13.4 kg
This is the maximum weight, because much of the volume we calculate is air that has a much lower density
W = 13.4 * 9.8
W = 131.3 N
Let's make the comparison by saying the two magnitudes
Side 1
F1 / W = 1999.8 / 131.3
F1 / W = 15.2
Side 2
F2 / W = 4545 / 131.3
F2 / W = 34.6
Side 3
F3 / W = 2778 / 131.3
F3 / W = 21.2
c) the cans do not collapse because the pressure is applied on both sides: outside and inside, so the net force is zero on each side.
