#1. The pressure P of a compressed gas is inversely proportional to the volume V. If there is a pressure of 35 pounds per square inch when the volume of gas is 400 cubic inches, find the pressure when the gas is compressed to 100 square inches.
#2. A frictional force is necessary for a car to round a bend. The frictional force, F kilonewtons, varies directly as the square of the car's speed, V meters per second, and inversely as the radius of the bend, R meters. Write down a relationship between F, V and R.
pressure P varies inversely with the volume V ---> P = k/V
when P=35, V - 400
35 = k/400
k = 35(400) = 14000
so P = 14000/V
I will assume you meant to say 100 cubic inches at the end of the first problem
so when V = 100
P = 14000/100 = 140
#1. To solve this problem, we can use the concept of inverse proportionality.
We are given that the pressure P of the gas is inversely proportional to the volume V. In mathematical terms, this can be expressed as P ∝ 1/V.
We also have the initial condition that when the volume V is 400 cubic inches, the pressure P is 35 pounds per square inch. Using this information, we can set up a proportion:
P1/V1 = P2/V2
Substituting the given values, we have:
35/400 = P2/100
Now, we can solve for P2 by cross-multiplying:
P2 = (35/400) * 100
Simplifying the right side gives:
P2 = 8.75 pounds per square inch
Therefore, the pressure when the gas is compressed to 100 cubic inches is 8.75 pounds per square inch.
#2. The relationship between the frictional force F, the car's speed V, and the radius of the bend R can be expressed using the principles of direct and inverse proportionality.
We are given that the frictional force F varies directly as the square of the car's speed V and inversely as the radius of the bend R. In mathematical terms, this can be written as:
F ∝ V^2 / R
To make it an equation, we introduce a constant of proportionality k:
F = k * V^2 / R
Here, k represents the proportionality constant. The value of k would depend on the specific conditions of the situation or experiment being performed.
Therefore, the relationship between F (frictional force), V (car's speed), and R (radius of the bend) can be expressed by the equation F = k * V^2 / R.