Calculate Motion Parameters: Environmental vs. Drag Force

[Student1989]

Homework Statement

An object is influenced by 2 forces: environmental force F1 = 42 tons and a hydrodynamic drag factor F2 = 200 kN. These forces are directed against each other (one attempting to 'weaken' the other one). The corresponding mass of object is 10,112 tonnes. I am trying to create a speed-time diagram - v(t) - showing the effect of the two forces on the movement of the object. Furthermore, I need to calculate the speed of the object upon reaching a distance of x metres (where x - any chosen distance).

Homework Equations

Limit velocity:
Vlim = √(V1/V2)

speed calculation:
m ⋅ ΔV = F ⋅ t
ΔV = (F1 ⋅ t) / m

acceleration vs. distance:
s = (a ⋅ t²)/2

others:
?

The Attempt at a Solution

for the environmental force (F1):
F1 = 42 [t] = 42 [t] ⋅ 9.81 [kg⋅m/s²] = 412.02 kN
Δ V1 = (412.02 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.041 ⋅ t [m/s]

for the drag force (F2):
F2 = 200 kN
Δ V2 = (200 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.020 ⋅ t [m/s]I obtained two values of acceleration and velocity resulting from the two forces F1 and F2 separately. Since they have opposite directions, I tried to calculate as following:

t ⋅ (0.041-0.020)

I figured that it's wrong, because the velocity cannot go towards infinity (because of the drag force acting), rising only to the limit velocity:

Vlim = √(V1/V2) = √(0.041/0.020) ≈ 1,432 [m/s]. What mistake do I make in the calculation?A helpful tool would be a ready v(t) diagram under this link:

h ttp://img401.imageshack. us/img401/6659/wykresm.jpg

It is created for the given variables. I am trying to figure out "how did they do that", i.e. what is the procedure involved, in order to create my own diagram for another object with different mass and the values of acting forces.

 

[jbsteele]

The procedure for creating the v(t) diagram is as follows:1. Calculate the acceleration due to the environmental force (F1) and the drag force (F2):For the environmental force (F1):F1 = 42 [t] = 42 [t] ⋅ 9.81 [kg⋅m/s²] = 412.02 kNa1 = (412.02 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.041 [m/s²]For the drag force (F2):F2 = 200 kNa2 = (200 [kN] ⋅ t {time}) / 10112 t {mass of object} ≈ 0.020 [m/s²]2. Calculate the limit velocity (Vlim) based on the two accelerations:Vlim = √(a1/a2) = √(0.041/0.020) ≈ 1,432 [m/s]3. Use the equations for acceleration vs. distance (s = (a ⋅ t2)/2) and speed calculation (ΔV = (F1 ⋅ t) / m) to plot the v(t) diagram:s = (0.041 ⋅ t2) / 2 v = 0.041 ⋅ t4. Calculate the speed of the object upon reaching a given distance (x metres):v = (x/t) + 0.041 ⋅ twhere t is the time it takes for the object to reach the distance x. This method can be used to create any v(t) diagram for an object influenced by two forces.