# Calculating Force in Freefall with Terminal Velocity

• sweenep
In summary, if a body is in freefall and has reached its terminal velocity, its acceleration is zero. To work out the force the body would hit the ground, you need to know the terminal velocity, that velocity divided by the time the body took to come to rest on hitting the ground. If you are given the distance of impact (depth of crater), you can use kinematics and dynamics to calculate the force.
sweenep
If a body is in freefall and has reached its terminal velocity say 56 metres/s, its acceleration is zero, how do you work out with what force it would hit the ground

you know the terminal velocity,that velocity divided by the time the body took to come to rest on hitting the ground would be the force with which it would hit the ground

sweenep said:
If a body is in freefall and has reached its terminal velocity say 56 metres/s, its acceleration is zero, how do you work out with what force it would hit the ground
Should be just mass of falling object times speed with which it impacts. You should probably, for the sake of simplicity, assume that the landing area has no elastic properties. The force would be the same even if the thing lands in a bowl of Jell-O, but it would be distributed a lot differently.

Last edited:
Beg your pardon, but the last two responses are incorrect.

If you have the initial speed of impact, you will need the mass of the object PLUS either the distance that the object went onto the ground during impact, or the time interval of the impact with the ground.

IF you have the time of the impact, F = mv/t , where v is the "change in velocity" (final velocity is zero). This is using the impuolse-momentum theorem.

If you are given d, the distance of impact (depth of crater), F = (mv^2)/2d
This is using kinematics and dynamics

well hello!your first option is what I wrote!

Your response is missing the mass of the object. The initial velocity divide by time of impact (assuming final velocity is zero) gives the acceleration. Multiply acceleration times mass to get force.

nishant said:
Shhh! It happens.

it better not happen often

Well, if I had a nickel for every mistake I've made in responding here, heck, I'd have fifteen cents by now.

Chi Meson said:
Beg your pardon, but the last two responses are incorrect.
I cannot believe that I confused 'force' and 'energy'. Sorry, guys. The terms just kind of swapped places in my head and I didn't notice. It's like when I'm stuck on a crossword puzzle answer for hours, then suddenly realize that I've misread the clue eight times in a row. (In my defense, I was on my 7th beer at the time.)

## 1. How do you calculate force in freefall with terminal velocity?

To calculate force in freefall with terminal velocity, you can use the formula F = mg - bv, where F is the force, m is the mass, g is the acceleration due to gravity, b is the drag coefficient, and v is the velocity. Alternatively, you can also use the formula F = ma, where F is the force, m is the mass, and a is the acceleration, which can be calculated by subtracting the drag force (Fdrag = bv) from the force of gravity (Fg = mg).

## 2. What is terminal velocity and how does it affect force in freefall?

Terminal velocity is the maximum velocity that an object can reach when falling through a fluid, such as air. When an object reaches terminal velocity, the force of gravity is balanced by the force of drag, resulting in a constant velocity. This means that the force in freefall will also become constant, as there is no longer any acceleration.

## 3. How does the mass of an object affect the force in freefall with terminal velocity?

The mass of an object has a direct effect on the force in freefall with terminal velocity. The greater the mass of an object, the greater the force of gravity acting on it. This means that a heavier object will experience a greater force in freefall compared to a lighter object, assuming they both have the same drag coefficient and are falling in the same fluid.

## 4. Can you calculate force in freefall with terminal velocity for objects falling in different fluids?

Yes, the formula for calculating force in freefall with terminal velocity can be used for objects falling in different fluids. However, the drag coefficient (b) will vary depending on the fluid's density and the object's shape and size. This means that the force in freefall may differ for the same object falling in different fluids.

## 5. What factors can affect the force in freefall with terminal velocity?

The force in freefall with terminal velocity can be affected by several factors, including the mass and shape of the object, the density and viscosity of the fluid, as well as external factors such as wind and air pressure. These factors can all impact the drag force acting on the object, which in turn affects the overall force in freefall.

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