Differential free falling bodies

In summary, we discussed solving the problem of an object of mass 10 kg being dropped from a great height with air resistance equivalent to 10 times the instantaneous velocity. We determined the velocity and distance the object would drop after 5 seconds using differential equations and the separation of variables method. We also considered the effects of mass on the equation.
  • #1
darthxepher
56
0
(i) how you solved this problem,

An object of mass 10 kg is dropped from a great height. (a) If the object is subjected to air resistance equivalent to 10 times the instantaneous velocity, find the velocity. (b) How far does the object drop after 5 sec?

(ii) what you got as a solution,

Don't know how to start. But i know you use differential equations.

(iii) why you think that is wrong.
 
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  • #2
try writing what the force or acceleration is at any given instant...
 
  • #3
Would it be 10(dv/dt)=98-10v?
 
  • #4
looks ok to me, now mass drops out of the equation, as it mulitplies every term..

now you can look at solving, probably a good place for separation of variables - what do you think?
 

Related to Differential free falling bodies

1. What is the concept of differential free falling bodies?

The concept of differential free falling bodies is based on the principle of gravitational acceleration, where two objects of different masses are dropped from the same height and fall towards the ground at the same rate. This means that the acceleration due to gravity is constant and independent of the mass of the object.

2. How is the motion of differential free falling bodies described?

The motion of differential free falling bodies is described by the equations of motion, specifically the equation for acceleration: a = g = 9.8 m/s^2. This means that the velocity of the objects will increase by 9.8 m/s every second until they reach the ground.

3. What is the significance of differential free falling bodies in physics?

Differential free falling bodies play a crucial role in understanding the laws of motion and gravity in physics. It helps us understand the concept of acceleration due to gravity and how it affects objects of different masses in the same way.

4. What factors can affect the motion of differential free falling bodies?

The motion of differential free falling bodies can be affected by factors such as air resistance, which can slow down the rate of acceleration, and the location on Earth, as the acceleration due to gravity can vary slightly based on altitude and latitude.

5. How does the height from which the objects are dropped affect the motion of differential free falling bodies?

The height from which the objects are dropped does not affect the motion of differential free falling bodies. As long as the objects are dropped from the same height, they will fall towards the ground at the same rate, regardless of their mass.

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