A storm approaches and the air pressure outside your apartment suddenly drops to 0.960 ✕ 105Pa from 1.013 ✕ 105Pa. Before the pressure inside your apartment has had time to change, what is the magnitude of the net force exerted on a window that measures 2.0 m x 2.8 m?
area = 2 * 2.8 = 5.6 m^2
force = area * difference in pressure
= 5.6 * (1.013 - .96) * 10^5
= .297 * 10^5 Newtons
= 2.97*10^4 Newtons
that is about the weight of a 3000 kg mass.
the window is history
Thanks so much
To determine the net force exerted on the window, we can use the equation:
Net Force = Pressure Difference x Area
Given:
Pressure Difference (ΔP) = 1.013 ✕ 10^5 Pa - 0.960 ✕ 10^5 Pa
Area (A) = 2.0 m x 2.8 m
First, let's calculate the pressure difference:
ΔP = 1.013 ✕ 10^5 Pa - 0.960 ✕ 10^5 Pa
ΔP = 0.053 ✕ 10^5 Pa
Now, we can calculate the net force:
Net Force = ΔP x A
Net Force = 0.053 ✕ 10^5 Pa x (2.0 m x 2.8 m)
Multiplying the values:
Net Force = 0.053 ✕ 10^5 Pa x 5.6 m^2
Net Force = 0.2968 ✕ 10^5 Pa⋅m^2
Simplifying:
Net Force = 2.968 ✕ 10^4 N
Therefore, the magnitude of the net force exerted on the window is approximately 2.968 ✕ 10^4 Newtons.
To determine the magnitude of the net force exerted on the window, we can use the concept of pressure and area.
1. Start by calculating the pressure difference caused by the storm:
ΔP = P2 - P1
ΔP = (0.960 ✕ 10^5 Pa) - (1.013 ✕ 10^5 Pa)
ΔP = -0.053 ✕ 10^5 Pa (note the negative sign indicates a decrease in pressure)
2. Next, calculate the force exerted on the window using the relationship between pressure, force, and area:
F = ΔP × A
F = (-0.053 ✕ 10^5 Pa) × (2.0 m × 2.8 m)
F = -2.968 ✕ 10^5 N
Therefore, the magnitude of the net force exerted on the window is approximately 2.968 ✕ 10^5 N. Note that the negative sign indicates that the force is directed inward, towards the apartment.