In the thermodynamics video I watched, it was stated that objects at higher elevations have more energy. And that objects must speed up as they fall. My question is, "what happens if an object reaches it's terminal velocity? It's still falling but no longer speeds up" Doesn't this make the statement that "objects must speed up as they fall", incorrect?
Asked
Active
Viewed 1,460 times
6 Answers
6
Only in a vacuum do falling objects continue to speed up the whole time they are falling. in air, they achieve constant velocity when the kinetic energy gain in descending matches the energy loss due to drag.
Roger V.
- 68,984
niels nielsen
- 99,024
4
No, it doesn't make the statement incorrect. It only it makes true for specific situations.
It is always true that in a system where there is no resistance, a falling object hits the ground with kinetic energy that depends on how high it was prior to being let go. Specifically, $$E_k=\frac 12mv^2=mgh$$ is how much kinetic energy it hits the ground with if there is no resistance. Note that this is equal to its potential energy as its dropped.
It is a fair question to ask, "well if an object has a certain amount of gravitational potential energy and is released, but then reaches a point where it can no longer accelerate, then where does the potential energy that should have been converted to kinetic energy, go?"
The answer is of course, it is converted into heat (heating the object and atmosphere) due to the frictional forces of the air$^1$.
$^1$ What's happening is that as the object is falling, it is colliding with the atoms/molecules in the atmosphere, and each time this happens, kinetic energy is transferred between the object and particles. If you had a very advanced machine that could calculate the kinetic energy of the object and particles before and after each collision, the total kinetic energy of the entire system (collisions + kinetic energy on impact with ground) will equal the initial gravitational potential energy.
joseph h
- 31,821
2
No, given statement is correct, because it assumes an ideal situation - free fall in a vacuum and only under influence of gravity all other forces excluded. All science is pretty much similar,- models abstracts unnecessary details away. Because only in this way we can extrapolate nature laws. Otherwise, if we would put each and every law and/or situation in one basket, we would get a chaos which would not help us to understand how nature operates in the nutshell at all.
You can get terminal speed from drag and weight equilibrium :
$$ {\tfrac {1}{2}}\,\rho \,v^{2}\,C_{D}\,A = mg $$
Upon reaching terminal speed, due to force(s) balancing weight,- body further falls at constant speed. Parachute is based on this idea,- it stops gravitational acceleration at low terminal speeds, because parachute has big cross-section area $A$, and hence produces high drag force.
Agnius Vasiliauskas
- 16,916
1
The statement "objects must speed up as they fall" is a bit of fast-and-loose casual conversation and not a definitive statement.
Generally speaking, these sorts of gravitational-potential energy problems are stated in Newtonian kinematic terms where "the force of gravity" is acting upon a falling object that has mass. Because "$F_{grav}=ma$" one might say that this gravitational force causes an acceleration of the mass, and thus a "speed up", but this is assuming the absence of all other forces.
In more complex situations with additional forces (like the normal force of a table surface, air friction in freefall, etc.) acting upon the object, it will be the case that $F_{total}\neq F_{grav}$ and thus the overall acceleration of "$F_{total}=ma$" might be positive, zero, or even negative depending upon the relative magnitudes and directions of all the forces involved.
DotCounter
- 150
1
All physical laws are simplified descriptions of reality. How much simplification is too much? How much error can you tolerate?
If you want to know how long it takes a cobble stone to fall from a second story window to the ground below, you can ignore the air resistance. It won't make enough of a difference for you to measure unless you measure timing, height, and initial velocity with high-precision instruments.
If you want to know how long it takes an inflatable beach toy to fall to Earth from an aircraft, then you can ignore Newton's laws altogether, and just base your answer on the altitude from which the toy was dropped and its terminal velocity.
For situations in between those two extremes, you may need to use a more complicated method that combines both Newtwon's laws and aerodynamic laws.
Solomon Slow
- 17,057
-4
Force is spatial rate of energy transference. When it is applied on an object, the object gains momentum or loss depending upon state of motion of an object and direction of applied force. It is never become constant instantaneously. When it becomes constant that means an object reach at equilibirium and rate of gain in momentum equals rate of loss in momentum.
Just like thermal equilibirium in which rate of absorption equals to rate of emission there is mechanical equilibirium in which rate of gain of momentum equals to loss of momentum. At mechanical equilibirium, an object attains constant speed. For mathematical expression visit link below.
