In this lab. you\'ll predict the motion of an object under the Influence of a re

Question

In this lab. you'll predict the motion of an object under the Influence of a resistive force (air resistance) that depends on the velocity. Remember the "update formulas" in class that follow directly from the definitions of velocity and acceleration: and we'll again use the clever technique of calculating the velocity halfway through the timestep (which is. in general, not quite the same as the average during the timestep). This is called the Leapfrog method. Remember that the resistive force due to the atmosphere is F = 1/2 C rho Av^2 so you can find the acceleration each time step by dividing that force by the mass of the falling object. Suppose the initial velocity is 0 (we're just dropping it) and it's a sphere, so we'll use C = 0.5. To make things easy, suppose we drop it at y = 0 and call the "down" direction positive (that's why the resistive force above has a negative sign), so we won't hast* to deal with negative displacements (so use g = 9.81 m/s^2). Now die resistive force will be directed up. so each time step you'll want to subtract it from g. Object data: m = 0.1 kg. r = 10 cm (it's a plastic beach ball), and air has a density of Take your time steps to be Delta t = 0.1 s. For the leapfrog method, well need the velocity at the first half-timestep v(10.05) =- a Delta t = (9.81M0.05) = 0.4905m/s So off we go: first calculate die position and new acceleration at t = 0.1 s. then the new v. then the new y, a. and so on. Now calculate 25 timesteps (to 2.5 seconds) and plot the position and velocity vs. time. From your velocity plot, estimate the terminal velocity, and compare that with the value you'd get from a direct calculation of vr = squareroot 2mg/CA rho. Is it close? Turn in your calculations. 2 plots, and comparison calculation.

Explanation / Answer

In this experiment we are noticing the velocity at different moment.
Before moving further we should know that what is the terminal velocity.
When our moving object will have the zero net force or start to move with constant velocity then that velocity is known as terminal velocity.
Forces on the object
gravity downward
Buoyancy upward
Air drag upward
out of these gravity and buoyancy forces are constant but the air drag will continue change because of the velocity of the object.
Once the summation the buoyancy and air drag equate the weight of the object then the velocity become constant of the object and that is terminal velocity.
Now when we check velocity at different time steps we notice increase in velocity but after some steps the velocity will be constant .
In your experiment , forces due to buoyancy is neglected therefore
Terminal velocity = (2mg/cAp)1/2
on putting the value we get = 5.1 m/s
Our acceleration will continuously change because of the air drag because of the increase in the air drag.
We calculate the velocity after each step and then we notice after some step that our velocity is not changeing which will be terminal velocity

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