speed and displacement of rocket?

Question

(hypothetical question)
If you have 1.8 gallons of gasoline, each which stores 100 mega Joules of energy which is released by burning the gas, and you could convert all the PE to KE of a rocket (60 kg).
☺ how fast would the rocket travel?
☺ if converted to gravitational PE how high could you fire the rocket?

can you show me how you got that so I can learn?

Answer 1

The important parameter in this problem is 100 mega joules total energy. You really don't care how much gasoline was used to generate the energy, just how much energy was generated. That energy is 100 mega joules = 100 x 10^6 joules = 10^8 joules.
A joule by definition is a Newton meter, and a Newton is a unit of force which is a mass times an acceleration, or kg m/sec^2. So a joule is 1 kg m^2/sec^2. So the total energy is 10^8 kg m^2/s^2.
First find KE. KE = 1/2 mv^2. Set total energy = KE, for a 60kg mass.
10^8 = 1/2 (60) v^2
Solve for v = 5774 m/s

If all that KE is converted to PE, then find h, height.
PE = mgh, and KE = 1/2 mv^2
PE = KE
mgh = 1/2 mv^2
h = 1/2 v^2/g, where g = 9.8 m/s2 = acceleration of gravity
= 1/2 (5774)^2/9.8
h = 1.7 x 10^6 m = ht of rocket

Answer 2

Yeah, I'd like to see how the answer was gotten, too.

In fact, there are too many data missing to really work your problem. Here's why.

You gave the potential energy of the gas P(0) on the launch pad. That will be converted to kinetic energy K(d) at some vertical height d through the work function P(0) = J = fd = (T - W)d; where T is the thrust and W is the weight of the rocket w(r) and the gas w(g). f is the net force acting over the distance d to convert P(0) into K(d).

Although we can specify that K(d) = P(0) by invoking the conservation of enery we cannot say what that d will be. That's because d = P(0)/(T - W) = K(d)/(T - W) and, as you can see, more thrust means shorter d and less weight over time means more d.

Houston, we have a problem. First, we have no thrust given. Thrust depends on the fuel and on the engine design as well.

Second, the net force f = Ma; where M = m(r) + m(g) = the total mass, which consists of the fixed rocket mass and the variable gas mass. m(g) diminishes as the gasoline is burned up. And you did not provide the specific impulse or burn rate for the gasoline.

When you make up a question, you need to ensure you've given enough information to work the answer.

Answer 3

If each gallon of gas stores 100 x10^6 J of energy, and it can be converted to KE of a 60 kg rocket, then:
(1/2)mv^2 = (1.8)(100x10^6J)
(1/2)(60kg)v^2 = 1800 x 10^6 J
30 v^2 =
v^2 = 600 x 10^6
v = 7.75 x 10^3 m/s

If converted to gravitational energy, U, how high would it go?

U =mgh
so h = U/mg
=(1800 x 10^6 J)/(60kg)(9.8m/s^2)
= 3 x 10^6 meters approximately

Answer 4

182.574 m/s
1700.68 m