What is the mathematical relationship bewtween pressure and displacement?

In summary, the question is asking about the relationship between pressure, speed, and displacement in a scenario where a large truck passes by a car stopped at an intersection turn lane. The correct answer is A) pulled towards the truck, because the increased wind speed between the truck and the car lowers the pressure there. This can be explained using Bernoulli's equation and the understanding that as velocity increases, pressure decreases. Additionally, the relationship between pressure and force is relevant in this scenario.
  • #1
tenbee
15
0

Homework Statement


I'm having trouble understanding the relationship between pressure, speed, and displacement to answer the following question correctly:

While you are stopped at an intersection turn lane, a large truck zooms by, just a few feet from your car. As the truck passes, your car will be:

A) pulled towards the truck, because the increased wind speed between the truck and the car lowers the pressure there.
B) pushed away from the truck, because the increased wind speed between the truck and the car lowers the pressure there.
C) pulled towards the truck, because the increased wind speed between the truck and the car increases the pressure there.
D) pushed away from the truck, because the increased wind speed between the truck and the car increases the pressure there.

Correct Answer: A

Homework Equations



Bernoulli's equation P + ρgy +1/2ρv^2 = K where P is pressure and ρ is density

The Attempt at a Solution




I was able to rule-out C and D from Bernoulli's equation P + ρgy +1/2ρv^2 = K where P is pressure and ρ is density... as velocity or speed increases, P must decrease. Now physically I've seen this exact scenario happen in slow motion (on some luxury car commercial), but mathematically I do not see the relationship between P and displacement.

Using equations without calculus, please demonstrate the relationship between pressure and displacement.
 
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  • #2
"pushed" and "pulled" relate to force, not displacement. If the pressure between you and the truck is less than the pressure on the other side of you, is the force going to be towards the truck or away from the truck? That part of the question is about the relation between pressure and force.
 
  • #3
Dick said:
"pushed" and "pulled" relate to force, not displacement. If the pressure between you and the truck is less than the pressure on the other side of you, is the force going to be towards the truck or away from the truck? That part of the question is about the relation between pressure and force.

AHHHHHHH... yes, yes - I forgot about the force on the other side of the car! Thanks so much.
 

Related to What is the mathematical relationship bewtween pressure and displacement?

1. What is the mathematical definition of pressure?

The mathematical definition of pressure is the force per unit area exerted on an object. It is typically denoted by the symbol P and has units of Newtons per square meter (N/m2) in the SI system.

2. How is displacement related to pressure?

Displacement is directly proportional to pressure. This means that as pressure increases, displacement increases and vice versa. This relationship is described by the equation P = kx, where k is a constant value.

3. What is the formula for calculating pressure?

The formula for calculating pressure is P = F/A, where P is pressure, F is the force exerted on an object, and A is the area over which the force is applied.

4. How does pressure affect the behavior of gases and liquids?

Pressure has a significant effect on the behavior of gases and liquids. In gases, an increase in pressure leads to a decrease in volume, while a decrease in pressure leads to an increase in volume. In liquids, an increase in pressure leads to a decrease in density, while a decrease in pressure leads to an increase in density.

5. How is pressure measured?

Pressure can be measured using a variety of instruments, including barometers, manometers, and pressure gauges. These instruments typically measure the force applied to a given area and convert it into a pressure value using the appropriate units.

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