A meat baster consists of a squeeze bulb attached to a plastic tube. When the bulb is squeezed and released, with the open end of the tube under the surface of the basting sauce, the sauce rises in the tube to a distance h, as the drawing shows. Using 1.013 × 105 Pa for the atmospheric pressure and 1260 kg/m3 for the density of the sauce, find the absolute pressure PB in the bulb when the distance h is (a) 0.15 m and (b) 0.11 m.
Oh, a meat baster question! You really know how to spice things up! Let's baste in some humor while we solve it.
(a) When the distance h is 0.15 m, we have some "saucy" calculations to make. We know that the atmospheric pressure is 1.013 × 105 Pa and the density of the sauce is 1260 kg/m3. So, let's squeeze out the answer!
To calculate the absolute pressure PB in the bulb, we need to consider both the atmospheric pressure and the pressure due to the column of sauce in the tube. Since the column of sauce is submerging the open end of the tube, it creates a pressure difference.
Using the equation: PB = P atmosphere + ρgh
Where:
PB is the absolute pressure in the bulb,
P atmosphere is the atmospheric pressure,
ρ is the density of the sauce, and
g is the acceleration due to gravity.
So, plugging in the values: PB = 1.013 × 105 Pa + (1260 kg/m3) × 9.8 m/s2 × 0.15 m
Now let's pop out the calculator and voila! You should find the answer.
(b) When the distance h is 0.11 m, the baster is getting into some tight spots! Let's do the calculations with a "squeeze" of humor!
Using the same formula as before: PB = 1.013 × 105 Pa + (1260 kg/m3) × 9.8 m/s2 × 0.11 m
Now, let's do some quick math and "squeeze" out the answer!
Remember, laughter is the best seasoning for problem-solving. Enjoy your saucy calculations!
To find the absolute pressure in the bulb, we can use Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted undiminished to all portions of the fluid and the walls of its container.
Let's solve part (a) first:
(a) When the distance h is 0.15 m.
We are given:
atmospheric pressure (P₀) = 1.013 × 10^5 Pa
density of the sauce (ρ) = 1260 kg/m³
distance h = 0.15 m
To find the absolute pressure (P_B) in the bulb, we need to consider the pressure due to the height of the liquid, as well as the atmospheric pressure:
P_B = P₀ + ρgh
where:
P_B = absolute pressure in the bulb
P₀ = atmospheric pressure
ρ = density of the sauce
g = acceleration due to gravity
h = height of the liquid
Substituting the given values into the equation, we have:
P_B = 1.013 × 10^5 Pa + (1260 kg/m³) × (9.8 m/s²) × (0.15 m)
= 1.013 × 10^5 Pa + 1847.4 Pa
≈ 1.013 × 10^5 Pa + 1847 Pa
≈ 1.031 × 10^5 Pa
Therefore, the absolute pressure in the bulb when the distance h is 0.15 m is approximately 1.031 × 10^5 Pa.
Now let's solve part (b):
(b) When the distance h is 0.11 m.
Using the same equation as before:
P_B = P₀ + ρgh
Substituting the new value of h, we have:
P_B = 1.013 × 10^5 Pa + (1260 kg/m³) × (9.8 m/s²) × (0.11 m)
= 1.013 × 10^5 Pa + 1356.84 Pa
≈ 1.013 × 10^5 Pa + 1357 Pa
≈ 1.0144 × 10^5 Pa
Therefore, the absolute pressure in the bulb when the distance h is 0.11 m is approximately 1.0144 × 10^5 Pa.
To find the absolute pressure PB in the bulb, we need to consider the pressure due to the column of sauce inside the tube, as well as the atmospheric pressure.
(a) When the distance h is 0.15 m:
The pressure at any point in a fluid at rest is given by Pascal's law, which states that the pressure is the same at all points within an incompressible fluid.
To find the pressure due to the column of sauce at a depth h, we can use the equation for hydrostatic pressure:
P = ρgh
Where P is the pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and h is the height of the column.
Given:
ρ = 1260 kg/m3
g = 9.8 m/s2
h = 0.15 m
Using the given values, we can calculate the pressure due to the column of sauce:
P_sauce = ρgh
= (1260 kg/m3)(9.8 m/s2)(0.15 m)
≈ 1847 Pa
Now, to find the absolute pressure PB in the bulb, we need to add the pressure due to the column of sauce to the atmospheric pressure:
PB = P_sauce + Patm
Given:
Patm = 1.013 × 105 Pa
Using the given values, we can calculate the absolute pressure in the bulb:
PB = 1847 Pa + (1.013 × 105 Pa)
≈ 1.031 × 105 Pa
Therefore, when the distance h is 0.15 m, the absolute pressure PB in the bulb is approximately 1.031 × 105 Pa.
(b) When the distance h is 0.11 m:
We can follow the same steps as in part (a) to find the absolute pressure PB in the bulb.
Given:
ρ = 1260 kg/m3
g = 9.8 m/s2
h = 0.11 m
Using the given values, we can calculate the pressure due to the column of sauce:
P_sauce = ρgh
= (1260 kg/m3)(9.8 m/s2)(0.11 m)
≈ 1373 Pa
Now, we can find the absolute pressure PB in the bulb:
PB = P_sauce + Patm
Given:
Patm = 1.013 × 105 Pa
Using the given values, we can calculate the absolute pressure in the bulb:
PB = 1373 Pa + (1.013 × 105 Pa)
≈ 1.026 × 105 Pa
Therefore, when the distance h is 0.11 m, the absolute pressure PB in the bulb is approximately 1.026 × 105 Pa.