Terminal Velocity of Ice Pellet: Homework Solutions

In summary, to find the terminal speed of the ice pellet, we can use the equation for drag force (FD = (1/2) * C * A * p * V^2) and equate it to the weight of the pellet (Fg = m * g). The mass can be found using the density of ice and the volume of a sphere. Once we have the mass, we can solve for velocity using the rearranged drag equation. To find the acceleration at 1% of the terminal speed, we can use the equations of linear motion and plug in the values for velocity and time.
  • #1
JJBlaze
1
0

Homework Statement


An ice pellet drops from a cloud 1.5 km above the Earth's surface. It's spherical so its drag coefficient is 0.45 and it has radius 0.1 mm. The density of air is 1.2 kg/m^3 and the density of ice is 910 kg/m^3.
What is the terminal speed of the ice pellet?
When the pellet is falling at 1% of its terminal speed, what is the magnitude of its acceleration?


Homework Equations


Volume of a sphere= (4/3)(pi)r^3
D=m/v
FD=(1/2)CAP(V^2)



The Attempt at a Solution


I've tried using D=m/v to solve for the mass of the ice pellet. So (910=m/.000418) and then taking this information and rearranging the FD equation to plug into V^2=square root((2 * m * g) / (Cd * r * A). As you move toward terminal velocity FD=w so FD=mg. I used the mass I got and plugged into that to give me FD and then plugged into the FD equation to solve for V^2 but that wasn't it either. I'm not sure what to do since I do not know FD, Velocity or the mass.
Thanks for your help!
 
Physics news on Phys.org
  • #2
The mass of the pellet should be constant (assuming no melting as it falls). How could you not obtain for the mass knowing the density of ice and the size of the pellet? All else is irrelevant to this calculation.

The drag force is proportional to the square of the velocity, so it's going to change over time until terminal velocity is reached.

To analyze this situation properly, you need to draw a free body diagram of the falling pellet. Then, you've got to apply the equations of linear motion to the problem.
 
  • #3
JJBlaze said:

Homework Statement


An ice pellet drops from a cloud 1.5 km above the Earth's surface. It's spherical so its drag coefficient is 0.45 and it has radius 0.1 mm. The density of air is 1.2 kg/m^3 and the density of ice is 910 kg/m^3.
What is the terminal speed of the ice pellet?
When the pellet is falling at 1% of its terminal speed, what is the magnitude of its acceleration?


Homework Equations


Volume of a sphere= (4/3)(pi)r^3
D=m/v
FD=(1/2)CAP(V^2)



The Attempt at a Solution


I've tried using D=m/v to solve for the mass of the ice pellet. So (910=m/.000418) and then taking this information and rearranging the FD equation to plug into V^2=square root((2 * m * g) / (Cd * r * A). As you move toward terminal velocity FD=w so FD=mg. I used the mass I got and plugged into that to give me FD and then plugged into the FD equation to solve for V^2 but that wasn't it either. I'm not sure what to do since I do not know FD, Velocity or the mass.
Thanks for your help!
Pls don't post just a summary of the steps you took. Post the actual working.
 

FAQ: Terminal Velocity of Ice Pellet: Homework Solutions

What is terminal velocity?

Terminal velocity is the maximum speed that an object can reach when falling through a fluid, such as air or water. It occurs when the force of gravity pulling the object down is equal to the force of air resistance pushing against it.

How is terminal velocity calculated?

The formula for calculating terminal velocity is v = √(2mg/ρAC), where v is the terminal velocity, m is the mass of the object, g is the acceleration due to gravity, ρ is the density of the fluid, A is the cross-sectional area of the object, and C is the drag coefficient. However, in the case of ice pellets, we can simplify this formula to v = √(2gd), where d is the diameter of the ice pellet.

How does the shape and size of an object affect its terminal velocity?

The shape and size of an object can greatly affect its terminal velocity. Objects with a larger surface area, such as flat objects, will experience more air resistance and therefore have a lower terminal velocity. On the other hand, objects with a smaller surface area, such as a sphere, will have a higher terminal velocity since they experience less air resistance.

How does air temperature affect the terminal velocity of ice pellets?

The temperature of the air can affect the terminal velocity of ice pellets. As the air gets colder, it becomes denser, which can increase the air resistance and therefore decrease the terminal velocity of the ice pellets. On the other hand, warmer air is less dense and will result in higher terminal velocities for the ice pellets.

What other factors can affect the terminal velocity of ice pellets?

Other factors that can affect the terminal velocity of ice pellets include the shape and density of the ice pellets, the altitude at which they are falling, and the presence of wind or other air currents. Additionally, the terminal velocity may vary for different types of ice pellets, such as hail or sleet, due to differences in their composition and size.

Similar threads

Constant Ratio of Drag coefficient and terminal velocity
Replies
5
Views
2K
How do I find the terminal speed of a body in water?
Replies
13
Views
4K
Terminal Velocity of a Cylinder Freefalling Through a Fluid
Replies
6
Views
9K
How come "terminal velocity" and "final velocity" are different?
Replies
1
Views
2K
Pellet fired through one foam block, embeds in second block
Replies
5
Views
1K
Terminal velocity of a skier using a Momentum Balance
Replies
1
Views
1K
Calculating the terminal velocity of a magnet falling through a copper coil
Replies
3
Views
2K
Terminal Velocity of 100kg Parachutist Falling from 3000m
Replies
4
Views
2K
Dimensional Analysis: Terminal Velocity
Replies
5
Views
10K
How Is Terminal Velocity Calculated in a Submerged Block System?
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top