Pressure~Gas Law Homework - Find Avg Pressure

[clovergogo]

Homework Statement

rain is falling normally on a circular region of radius 25cm at a rate of 1.2gs-1
suppose the velocity of each raindrop just before it reaches the region is 10cms-1
and the collision between each raindrop and the region is perfectly elastic
find the avg pressure exerted on the region

take g=9.8ms-1

Homework Equations

P= F/A

The Attempt at a Solution

momentum, then the Pressure
is it ...P = (0.0012X10+0.0012X9.8) / 0.25^2 pi??

 

[Andrew Mason]

Homework Statement

rain is falling normally on a circular region of radius 25cm at a rate of 1.2gs-1
suppose the velocity of each raindrop just before it reaches the region is 10cms-1
and the collision between each raindrop and the region is perfectly elastic
find the avg pressure exerted on the region

take g=9.8ms-1

Homework Equations

P= F/A

The Attempt at a Solution

momentum, then the Pressure
is it ...P = (0.0012X10+0.0012X9.8) / 0.25^2 pi??

If the collisions are perfectly elastic, what is the change in momentum of a raindrop of mass m striking this area?

Now take N such raindrops every second such that Nm = 1.2 g. What is the total change in momentum of the raindrops every second? How is that change in momentum every second related to the force imparted to the circular area? What is that force/unit area?

AM

 

[clovergogo]

can i take t=1
then mv-mu/t = F can be count
then mass = 1.2 X 1
then Pressure (P) can be count

 

[ehild]

can i take t=1
then mv-mu/t = F can be count
then mass = 1.2 X 1
then Pressure (P) can be count

If you use the units and parentheses properly, the method will work. What is u if the collision is perfectly elastic?

ehild

 

[Nickie]

I would approach this problem by first understanding the concept of pressure and how it is related to force and area. Pressure is defined as the amount of force per unit area, and can be calculated using the equation P = F/A, where P is pressure, F is force, and A is area.

In this problem, we are given information about the rate of rain, the velocity of the raindrops, and the size of the circular region. To find the average pressure exerted on the region, we need to calculate the force that each raindrop exerts on the region and then divide by the area.

To calculate the force, we can use the equation F = ma, where F is force, m is mass, and a is acceleration. In this case, we are given the mass of the raindrop (1.2g) and the acceleration due to gravity (9.8ms^-2). Therefore, the force of each raindrop is 0.01176N.

Next, we need to consider the area over which the force is applied. Since the region is circular, we can use the equation for the area of a circle, A = πr^2, where A is area and r is the radius. In this case, the radius is given as 25cm, or 0.25m. Therefore, the area of the region is 0.1963m^2.

Now, we can plug these values into the equation for pressure, P = F/A, to find the average pressure exerted on the region. Substituting in the values we calculated, we get P = 0.01176N / 0.1963m^2 = 0.05985Pa.

Therefore, the average pressure exerted on the circular region is 0.05985 Pa. It is important to note that this is the average pressure, as the pressure may vary at different points on the region depending on the distribution of raindrops and their velocities.