Dropping objects air resistance

In summary, the problem involves a creature of mass m and bottom surface area A being dropped from a height h towards the ground. The creature will die if a force of F_K or greater acts on it. To determine the value range of acceleration due to gravity, g, for the creature to survive the fall, we can use the equation F_D = -k * v and solve for g in terms of F_K, h, m, and A. This may involve finding the terminal velocity and relating it to F_K and g. However, the softness of the ground must also be taken into consideration, potentially using the impulse formula and knowing the distance over which the fall was cushioned. The presence of A in the problem statement suggests
  • #1
Big-Daddy
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Homework Statement


A creature of mass [itex]m[/itex] and bottom surface area of [itex]A[/itex] is dropped from a height [itex]h[/itex] towards the ground. The creature dies if a force of [itex]F_K[/itex] or greater acts on it. What is the value range of acceleration due to gravity, [itex]g[/itex], for such creature to survive the fall?

Homework Equations



Surely the problem requires air resistance since mass and surface area are mentioned. I think this can be modeled as [itex]F_D=-k \cdot v[/itex] unless anyone has any better ideas?

The Attempt at a Solution



The question is what else to do - we'll need a differential equation, then to solve it for [itex]g[/itex] in terms of [itex]F_K[/itex], [itex]h[/itex], [itex]m[/itex] and [itex]A[/itex] (probably work out the terminal velocity first and then relate it to [itex]F_K[/itex] and [itex]g[/itex])? I hope we can assume that height [itex]h[/itex] is sufficient that terminal velocity will be reached. If not, we might have to use something more fundamental.
 
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  • #2
Depends on the softness of the ground. Use the impulse formula. F*Δt = Δp and Δt =√(2s/g). But you need to know s, the distance over which the fall was cushioned, i.e. the softness of the ground.

The presence of A in the problem statement does suggest that air resistance was to be considered. Could be a red herring. I would ignore it or get an explanation from the instructor.
 

1. What is air resistance?

Air resistance, also known as drag, is a force that opposes the motion of an object through air or any other fluid. It is caused by the friction between the surface of the object and the air molecules it comes in contact with.

2. How does air resistance affect the speed of a falling object?

Air resistance increases as the speed of a falling object increases, thus slowing down the object's motion. This is because as the object moves faster, it encounters more air molecules, resulting in a greater force of drag.

3. How does the shape of an object affect air resistance?

The shape of an object greatly affects the amount of air resistance it experiences. Objects with a streamlined shape, such as a cone or an airplane wing, experience less air resistance than objects with a more irregular shape, such as a feather or a crumpled piece of paper.

4. What is terminal velocity and how does it relate to air resistance?

Terminal velocity is the maximum speed that a falling object can reach when the force of gravity is equal to the force of air resistance. As an object falls, its speed increases until it reaches a point where the force of air resistance is equal to the force of gravity, causing it to stop accelerating and reach a constant speed.

5. How can air resistance be reduced?

Air resistance can be reduced by altering the shape of an object to make it more streamlined, reducing the surface area of the object, or increasing the object's mass. Additionally, air resistance can be reduced by decreasing the density of the air, as it will result in a lower number of air molecules for the object to encounter. This is why objects fall faster in a vacuum than in air.

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