How do you explain this, Equation?

[sl02ggp]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

 

[sl02ggp]

anyone?

 

[Mark44]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

If the person were falling in a vacuum, the differential equation would be dv/dt = g. The resistance to motion caused by the parachute (and the person's body) will lessen the acceleration, which explains the (k/m)v term being subtracted on the right (not ride) side.

Is that what you're asking about?

 

[HallsofIvy]

A person who weighs 200 lbs is falling through the sky while attached to a parachute. The equation of the downward velocity as a function of time for this is:

dv/dt = g - (k/m)v

Where g is the acceleration due to gravity, m the person's mass, and k is a constant depending on the physical properties of the parachute.

Question: How does this equation physically make sense? Where does the variables from the ride hand side come from?

Experimental evidence (which is the final arbiter in "real life" matters) indicates that for an large object moving through air, the air resistance (drag) is, at least approximately, directly proportional to the speed with which the object is moving. 0 speed would mean it is not moving through the air at all so no drag. If the object were moving upward, the resistance would be downward and if the object is moving downward the resistance would be upwared- always opposite to the motion hence the "-".

Starting from "mass times acceleration = total force" we would have m(dv/dt)= mg- kv. Dividing both sides by m, dv/dt= g- (k/m)v.

 

[blue_raver22]

This equation is known as the "equation of motion" for a falling object with air resistance. It takes into account the acceleration due to gravity, represented by g, and the effects of air resistance on the object's velocity, represented by the term (k/m)v.

The presence of air resistance is an important factor to consider when analyzing the motion of a falling object, especially if it is attached to a parachute. As the person falls, the parachute will create a force that opposes the downward force of gravity, slowing down the person's descent. This opposing force is proportional to the person's velocity and the physical properties of the parachute, hence the term (k/m)v in the equation.

The value of g is a well-known constant, representing the acceleration due to gravity on Earth. The value of k and m will vary depending on the specific properties of the parachute, such as its surface area and shape, and the person's mass. These variables can be determined through experiments or calculations based on the design of the parachute.

In summary, this equation makes physical sense because it takes into account the forces acting on the falling object and how they affect its velocity over time. The variables on the right-hand side of the equation represent the specific physical factors that contribute to the object's motion in the presence of air resistance.