# Physics question if you're interested

#### calbear2000

##### Golden Member
It has been almost 10 years since my last physics class... so I couldn't solve someone's problem for them:

A rocket has an empty weight of 500 lbs and carries 300 lbs of fuel. If
the fuel is burned at a rate of 15 lbs/sec and ejected with a relative
velocity of 4,400 ft/sec, determine the maximum speed attained by the
rocket starting from rest. Assume the rocket is in space and there is no
gravitational influence.

I'm thinking it reaches 4400ft/sec and stays there since there is no other force (ie gravity) accelerating or decelerating it... but its been a long time since I've stepped into a classroom.

#### Bound_Vortex

##### Member
I'm thinking there has to be something missing. The rocket is ejected at 4400 ft/s, implying that is the initial velocity. There must be some connection between the burn rate of the fuel and the effect that would have on the delta v. Otherwise the weight of the rocket and the fuel and the burn rate is meaningless. Ask what the effect is of the fuel being burned....energy is being created there, and it has to affect something.

#### dighn

##### Lifer
acceleration_rocket = force / mass
mass = initial_total_mass - masslostpersecond*t
force = dp/dt = mass_ejected_per_second*jet_velocity

acceleration = (4400*15 lb/sec ft/sec) / (800lb - 15lb/sec*t)

*i know lb is not unit of mass but u do the lb -> mass conversion, the constant of conversion canels out anyway. the final units are correct if u intergrate (ft/sec_)

now you have acceleration, intergrate once with respect to time and go from 0 seconds to 20 seconds

is this correct? i dunno so..

#### Bound_Vortex

##### Member
You jumped the gun on a few things here:
- the 800 lbs is a force not a mass, same with the 15
- I'm not sure what you did with your force line, but the units don't match up...the product of a velocity and a weight (a force) cannot be a force.
- your acceleration line has the units of a distance...from the 4400 ft/sec multiplied by time

Are we to assume that the fuel burn rate is actually correlates to the force...like burning 15 lbs of fuel produces 15 lbs of force? If so a number of equations could be formulated and integrated to find the maximum speed

#### dighn

##### Lifer
Originally posted by: Bound_Vortex
You jumped the gun on a few things here:
- the 800 lbs is a force not a mass, same with the 15
- I'm not sure what you did with your force line, but the units don't match up...the product of a velocity and a weight (a force) cannot be a force.
- your acceleration line has the units of a distance...from the 4400 ft/sec multiplied by time

Are we to assume that the fuel burn rate is actually correlates to the force...like burning 15 lbs of fuel produces 15 lbs of force? If so a number of equations could be formulated and integrated to find the maximum speed

eh i dunno much about the empirical system. i assumed lb = kg, ft/sec = m/sec etc. i guess you'll have to convert them to get it into the correct units. but i think once converted it should all work out.

lemmie look up the emprical constants stuff and modify it

#### dighn

##### Lifer
err forget it. i hate messing with the english system. replaced all the numbers with word descriptions...

as for the force, well force is the change in impulse per unit time. impulse is m*v. you can interprete it as dm/dt * v, where v is the final velocity of the gas particles and the dm/dt is how much gas particles is ejected per second. the gas particles have to push on the rcoetk to gain speed.

edit:

on second thought, the units are irrelevant. because assuming lb is a measure of force, there is a constant relating lb and the empirical mass unit (called slug?)

since i'm treating lb consistently as a mass unit and all the mass in the original problem are given as lb, the constant cancels out so it is fine

1 = .9

#### Moonbeam

##### Elite Member
How do you find out how much force of acceleration is supplied by 15 lb of fuel expelled at 4400 ft/sec? I don't know physics formulas, Is it force equals mass times velocity? Whatever it is it would seem then that after one second you could reverse the forumla using 792.5lb as the average weight of the rocket during that second to determine how fast the rocket is going after one second. Would it then be reasonable to say that in 20 seconds it would be going twenty times as fast?