Hardest AP PHysics lab EVERRRRRR

[the4thcafeavenue]

now guys, i need your help. in this lab, i am making a rocket with a 2 litter soda bottle with water inside, and air will be pumped in so that rocket will fly up. i need to determine a set of equations that will describe the THRUST of my rocket as a function of TIME or MASS or both. we can use M*(delta)v=dm*Ve and Vf-Vi=Ve*ln(Mi/Mf) and whatever other equations will help. Thrust= M(dv/dt) or Ve*(dM/dt).

 

[Justin Lazear]

Start with Newton's second law,

$$F = \frac{d}{dt} mv$$

and keep in mind that mass is no longer constant, so you must apply the chain rule.

$$F = \frac{d}{dt}\left( mv\right) = v\frac{dm}{dt} + m\frac{dv}{dt}$$

See what you can do from there.

--J

 

[wais]

Wow, that does sound like a challenging lab! I can definitely understand why you need some help with determining the equations for thrust. Let's break it down step by step.

First, we need to understand what exactly we mean by thrust. In this case, we are looking at the force that propels the rocket upwards. From Newton's second law, we know that force is equal to mass times acceleration (F=ma). In this case, the mass of the rocket is changing as the water is being expelled, so we need to take that into account.

Next, we can use the equation you mentioned, M*(delta)v=dm*Ve, which relates the change in velocity (delta v) to the change in mass (delta m) and the exhaust velocity (Ve). This equation is derived from the conservation of momentum, where the momentum of the rocket (mass times velocity) must be equal to the momentum of the expelled water (mass times exhaust velocity).

We can also use the equation Vf-Vi=Ve*ln(Mi/Mf), which relates the final velocity (Vf) to the initial velocity (Vi) and the exhaust velocity (Ve), taking into account the change in mass (Mi/Mf).

Combining these two equations, we can come up with an expression for the thrust as a function of time and mass: Thrust = Ve*(dm/dt) = M*(dv/dt).

In simpler terms, this means that the thrust of your rocket is equal to the mass of the water being expelled per unit time multiplied by the exhaust velocity, or it can also be expressed as the mass of the rocket times the rate of change of its velocity.

I hope this helps and good luck with your lab! Remember to double check your equations and units to make sure everything is consistent.