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 ?

accelerating force=ma

force opposing gravity=mg
Net forceapplied=sum=mg+ma

The reason why the formula used is FORCE = MASS (GRAVITY + ACCELERATION) instead of FORCE = MASS x ACCELERATION is because in this scenario, we are dealing with both the force due to gravity as well as the force produced by the propulsion system of the rocket.

The formula FORCE = MASS x ACCELERATION (F = ma) is commonly used to calculate the force acting on an object due to an applied external force or acceleration. However, in the case of a rocket escaping into space, we need to consider both the force due to gravity and the force exerted by the rocket's propulsion system.

Gravity is constantly pulling the rocket downward, and the force due to gravity is given by MASS x GRAVITY. Whereas, the force exerted by the rocket's propulsion system creates an upward force that accelerates the rocket upwards. This force is equal to MASS x ACCELERATION.

To calculate the total force of the escaped gases of the rocket, which is the net force acting on the rocket, we need to combine the force due to gravity and the force exerted by the propulsion system. Hence, the formula used is FORCE = MASS (GRAVITY + ACCELERATION).

To understand why the formula FORCE = MASS (GRAVITY + ACCELERATION) is used in this scenario instead of the formula force = mass x acceleration, we need to consider the forces acting on the rocket.

In the given problem, we are calculating the force exerted by the escaping gases of the rocket. This force is commonly referred to as the thrust force.

The thrust force is generated by the expulsion of gases from the rocket's engines, which creates a reaction force pushing the rocket forward. According to Newton's third law of motion, for every action, there is an equal and opposite reaction. Thus, the force exerted by the escaping gases is equal to the force experienced by the rocket in the opposite direction, i.e., the thrust force.

In order to determine the value of the thrust force, we need to consider two key components: the mass of the rocket (0.25 kg) and the net acceleration experienced by the rocket.

The net acceleration experienced by the rocket is the sum of two components: the acceleration due to gravity (g) and the acceleration caused by the expulsion of gases from the rocket (41.67 m/s^2, as calculated).

Now, let's break down the formula FORCE = MASS (GRAVITY + ACCELERATION):

FORCE = THRUST FORCE (Force exerted by the escaping gases)
MASS = MASS of the rocket (0.25 kg)
GRAVITY = Acceleration due to gravity (approximately 9.8 m/s^2)
ACCELERATION = Net acceleration experienced by the rocket (41.67 m/s^2)

By using this formula, we account for the contribution of the rocket's weight due to gravity and the additional acceleration caused by the escaping gases, resulting in a more accurate determination of the thrust force.

On the other hand, the formula force = mass x acceleration (F = ma) is a general formula used to calculate the force on an object due to its acceleration. It does not account for specific forces like the gravitational force acting on the object.

When analyzing the forces acting on an object, it is crucial to consider all relevant forces and their respective contributions. In this case, the formula FORCE = MASS (GRAVITY + ACCELERATION) appropriately accounts for both the gravitational force and the additional acceleration due to the rocket's propulsion system.