The question seems ambiguous. Is it the total impulse generated by the fuel that's wanted, or the effective impulse on the rocket? The second is quite easy.Alameen Damer said:Homework Statement
A 1990 kg rocket is loaded with 102 kg of propellant. It exhausts the propellant in a burn of 25s. The rocket starts at rest, and moves with a speed of 240 m/s after the burn. Determine the impulse.
Homework Equations
Impulse (p) = m1vf-m1vi
The Attempt at a Solution
How would one calculate the impulse given that the mass changes because of the loaded propellant which is used up by the time the mass hits the final velocity.
The description speaks of rocket and fuel as distinct, so no, it would not include the 102kg. That's what makes the question easy. If yiu had to include the 102kg you would not know what to put for final velocity. Relative to the ground, fuel expelled early would have a different velocity from that expelled later.Alameen Damer said:I would assume the effective impulse on the rocket, given that they talk about it speeding up, etc. If this is the case, using (p) = m1vf-m1vi, do I include the 102 kg propellant as part of the mass?
Halls, I'm not alone in regarding that formulation as misleading. It treats mass as an arbitrary variable, as though a moving object can acquire mass out of nowhere. In reality, the mass must come from or go to somewhere else. For the equation to work, that mass must not bring in or take out any momentum, i.e. when not part of the object it must be at rest in the reference frame. I wrote a homily on this in section 6 of https://www.physicsforums.com/insights/frequently-made-errors-mechanics-momentum-impacts/.HallsofIvy said:The basic rule is that force equals the derivative of momentum. If the mass is constant, that is "mass times the acceleration" but if mass is not constant, it is (mv)'= m'v+ mv'.
According to Newton's second law, an object's momentum is directly proportional to its mass. This means that as mass increases, so does momentum. Therefore, changing mass can have a significant impact on an object's momentum.
Yes, changing mass can affect an object's velocity. This is because velocity is also dependent on an object's mass, as shown in the equation v = p/m, where v is velocity, p is momentum, and m is mass. So, as mass changes, velocity will also change accordingly.
Changing impulse can affect an object's motion by altering its momentum. Impulse is the change in momentum, so a larger impulse will result in a larger change in momentum, and vice versa. This change in momentum will then affect the object's motion, such as its speed or direction.
No, changing impulse cannot result in a change in mass. Mass is an intrinsic property of an object and cannot be altered by external forces, such as impulse. However, changing impulse can result in a change in an object's momentum, which can then affect its mass according to Newton's second law.
Mass and impulse are both conserved quantities according to the law of conservation of momentum. This means that in a closed system, the total mass and total impulse will remain constant before and after any interaction. In other words, changing mass or impulse in one part of a system will cause an equal and opposite change in another part of the system.