A speed velocity of a a rocket with a mass of 0.25 kg passes from 15 m/s[up] to 40 m/s[up] in 0.60s. calculate the force of the escaped gasses of the rocket.
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that's what i've done, so far
data: m = 0.25kg
initial velocity = 15 m/s
final velocity = 40 m/s
time = 0.60s
final velocity - initial velocity / time = acceleration
40 m/s - 15 m/s / 0.60 s = 41.67 m/s^2
for here the solutions for the problem says that the next formula that needs to be used is FORCE = MASS (GRAVITY + ACCELERATION) why is that.
and why would you not use the formula
force = mass x acceleration ?
acceleration due to gravity must be factored in as the rocket is traveling upwards. since you have chosen up to be positive acceleration down must be negative, making gravity -9.8m/s
the equation is still
force=mass x acceleration
accept the formula used to calculate acceleration does not factor in gravity, the value calculated will just assume that no other forces are acting on the rocket
i know this may not be the best clarification so ask away with any problems :)
To answer your questions, let's understand the concept of force and how it relates to the situation of a rocket with escaping gases.
The force experienced by an object can be calculated using the formula:
Force = Mass x Acceleration
Where:
- Force is the net force acting on the object.
- Mass is the mass of the object.
- Acceleration is the rate of change of velocity experienced by the object.
In the case of the rocket, the escaping gases produce a force that propels the rocket forward. This force, known as the thrust force, is caused by the expulsion of gases with high momentum in the opposite direction.
However, we need to consider that in addition to the thrust force, the rocket is also subject to the force of gravity. So, when calculating the net force on the rocket, we need to take into account both the gravitational force and the thrust force.
The formula you mentioned, "Force = Mass x (Gravity + Acceleration)," is an extension of the basic formula to account for both forces. It considers that the acceleration experienced by the rocket is not only the rate of change of velocity due to the thrust force but also includes the acceleration due to gravity.
To calculate the thrust force, we need to use the formula:
Thrust Force = Mass x Acceleration
Where:
- Mass is the mass of the rocket.
- Acceleration is the rate of change of velocity experienced by the rocket.
In your case, you have already calculated the acceleration to be 41.67 m/s^2. So, you can use this value, along with the mass of the rocket (0.25 kg), to calculate the thrust force of the escaping gases:
Thrust Force = Mass x Acceleration
Thrust Force = 0.25 kg x 41.67 m/s^2
By multiplying these values, you should be able to calculate the force of the escaping gases for the given situation of the rocket.