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Gravitational force is a fundamental natural force that attracts two bodies towards one another. In the context of our rocket, it is the force pulling the rocket towards the Earth. We calculate gravitational force using the formula: \[ F_{gravity} = m imes g \]where:

• \( m \) is the mass of the object (in this case, the rocket) in kilograms.
• \( g \) is the acceleration due to gravity, approximately \( 9.8 \; \text{m/s}^2 \) on the surface of the Earth.

For the rocket, the gravitational force is computed as:\[ F_{gravity} = 125 \times 9.8 = 1225 \; \text{N} \]This calculation shows that the gravitational force acting downward on the rocket is 1225 Newtons. Understanding gravitational force helps in determining how much thrust is required to counteract it and achieve desired motion.

Thrust is the force exerted by the rocket's engine to propel it upwards, opposing the gravitational pull. It is critical in determining the rocket's ability to lift off the ground and accelerate into the air. In this exercise, the engine generates a constant thrust of 1720 Newtons.The thrust must outweigh the gravitational force for the rocket to ascend. By establishing a net force:\[ F_{net} = F_{thrust} - F_{gravity} = 1720 - 1225 = 495 \; \text{N} \]The net force is crucial because it is the unbalanced force that imparts acceleration to the rocket, according to Newton's Second Law. This interplay of forces illustrates how thrust allows the rocket to overcome gravity and initiate movement.

A free-body diagram is a visual representation of all the forces acting on an object. For the power supply in the rocket, it helps us understand the forces influencing it while the rocket is in motion. The diagram would include:

• The weight of the power supply pointing downward, which is a force of 15.5 Newtons due to gravity.
• The normal force from the floor of the rocket acting upward.

The normal force reflects how hard the floor "pushes back" against the power supply. When the rocket ascends, this force changes because of the additional acceleration due to the rocket’s upward movement. The modified weight or apparent weight can be calculated considering both gravitational force and the rocket's acceleration, giving a deeper insight into how forces act within moving vehicles.

The acceleration of a rocket is determined by applying Newton's Second Law, which states that the acceleration of an object is the net force acting upon it divided by its mass.For our rocket, the net force is 495 Newtons, as calculated from the thrust and gravitational force. The mass of the rocket is 125 kg. Thus, the acceleration can be calculated using the formula:\[ a = \frac{F_{net}}{m} = \frac{495}{125} = 3.96 \; \text{m/s}^2 \]This result means the rocket accelerates upwards at 3.96 meters per second squared. Acceleration dictates the change in velocity over time, which is crucial for reaching specific altitudes and controlling the vehicle's trajectory. Understanding acceleration is vital for predicting motion and designing effective propulsion systems.