Help with Drag Force/Terminal Velocity assignment

In summary: I am not sure if I provided the information correctly, but I am going to try to answer the questions. In summary, the object mass is 20 grams, the dimensions of the box are 15cm x 10cm x 8cm, the times to fall a distance of 5 meters are 1.95, 1.99, 2.03, 1.9, 2.06, 2.12, 2.05, 2.2, 2.07. The given data suggests that the terminal velocity is 2.07. Using the analytic formula, the terminal velocity can be determined to be 1.96.
  • #1
chris_0101
65
0
Hi, I am a Senior in High school, looking for some help with a couple of questions that deal with both physics and mathematics. I was given a sheet with 4 scenarios on it, I chose a box falling from a height of 5 meters. The information is shown below:

Object mass: 20 grams
Dimensions of box: 15cm x 10cm x 8cm
Times to fall a distance of 5 meters: 1.95, 1.99, 2.03, 1.9, 2.06, 2.12, 2.05, 2.2, 2.07. 1.96

The above are the given data, now my questions include the following:

1) Using the analytic formula, - d(t) = (VT^2 / g)ln[cosh(gt / VT)] - which we will assume to be correct. Determine the terminal velocity (VT).
- The question also states "Solving for VT is difficult, the following method would work more easily: Using a graphing calculator, graph the position function with VT being the unknown, and find when the function is equal to the total distance actually fallen (5m)"

With this question above, can someone please explain what a position function
is and how do I find the function equal to the total distance actually fallen

2) Now we want to find an approximating function for the velocity as a function of time. The area under the velocity time graph should be equal to the distance fallen. You have an estimate for the terminal velocity, but need to approximate the motion by assuming a constant acceleration until the terminal velocity is reached

For this question, I can basically sum it up to this, how do I this? Can someone
also please explain what an approximating function is and how to find it.

The two question above are more of steps that I need to accomplish in order complete the questions that I have, but I am pretty sure I can handle those on my own. Whoever, can answer my questions, Thank you so much.
 
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  • #2
Show some attempt.
 
  • #3
Ya, I did attempt it. I spent a whole day trying to figure this out.
 

1. What is drag force and how does it affect objects?

Drag force is a force that acts in the opposite direction of an object's motion through a fluid, such as air or water. It is caused by the resistance of the fluid against the object's surface. The magnitude of drag force depends on the object's size, shape, and speed.

2. What is terminal velocity and how is it related to drag force?

Terminal velocity is the maximum velocity that an object can reach in free fall due to the balance between the gravitational force and the drag force. As an object falls, the force of gravity increases its speed, while the drag force increases as the object's speed increases. Eventually, the two forces become equal and the object reaches a constant velocity, known as terminal velocity.

3. How do you calculate the drag force on an object?

The drag force on an object can be calculated using the equation Fd = 1/2 * ρ * v^2 * Cd * A, where Fd is the drag force, ρ is the density of the fluid, v is the velocity of the object, Cd is the drag coefficient, and A is the cross-sectional area of the object.

4. What factors affect the magnitude of drag force on an object?

The magnitude of drag force is affected by the density of the fluid, the velocity of the object, the shape and size of the object, and the fluid's viscosity. Objects with larger surface areas, higher velocities, and less streamlined shapes will experience greater drag force.

5. How does understanding drag force and terminal velocity help in real-world applications?

Understanding drag force and terminal velocity is important in various fields such as engineering, physics, and sports. It can help engineers design more efficient and aerodynamic structures, and it is crucial in predicting the performance of vehicles, aircraft, and sports equipment. Additionally, understanding these concepts can also help in understanding natural phenomena, such as the flight of birds and the movement of ocean currents.

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