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Gravitational acceleration is an important concept in physics that tells us how strong gravity is at pulling objects toward a planet's surface. This acceleration is usually symbolized by \(g\) and is measured in meters per second squared (m/s²). On Earth, \(g\) is approximately 9.8 m/s², but on other planets, it can vary widely.
To find a planet's gravitational acceleration, we use the relationship between an object's weight and its mass. Weight is simply the force with which gravity pulls on an object and can be calculated using the formula:

• \(W = m \cdot g\)

where \(W\) is the weight in Newtons (N), \(m\) is the mass in kilograms, and \(g\) is the gravitational acceleration in m/s².
In our problem, we found the gravitational acceleration of the mysterious planet by dividing the rock's weight (40.0 N) by its mass (5.00 kg). This gave us \(g = 8.0 \text{ m/s}^2\), indicating that this planet has a weaker gravitational pull compared to Earth.

Newton's second law of motion connects force, mass, and acceleration in a simple but powerful way. It is expressed by the equation \(F = m \cdot a\), where \(F\) is the force applied to an object, \(m\) is its mass, and \(a\) is the acceleration produced.
This law tells us that the acceleration of an object depends directly on the net force acting on it and inversely on its mass. A larger force will produce a greater acceleration, but a larger mass will make that acceleration smaller.
In our scenario, we needed to find the rock's acceleration when the astronaut applied an extra force upwards. By using the net force and the rock's mass, we rearranged the formula to solve for acceleration:

• \(a = \frac{F_{\text{net}}}{m}\)

Using the provided numbers, we calculated the net force to be 6.2 N and the rock’s mass is 5.00 kg, revealing that the rock's acceleration is \(1.24 \text{ m/s}^2\). This acceleration explains how quickly the rock speeds up as it moves away from the planet's surface.

Net force refers to the total force acting on an object after all the individual forces have been summed up, considering both their magnitudes and directions. It's crucial because it determines the resulting motion of the object.
When multiple forces work on an object, both the magnitude (how strong the forces are) and their directions matter. The net force is essentially this combination that dictates whether an object speeds up, slows down, stays still, or changes direction.
In our physics problem, the rock was influenced by two main forces:

• The rock's weight acting downwards (40.0 N)
• The upward force exerted by the astronaut (46.2 N)

To find the net force \(F_{\text{net}}\), we simply calculated the difference between these forces since they were in opposite directions:

• \(F_{\text{net}} = F_{\text{upward}} - W = 46.2 - 40.0 = 6.2 \text{ N}\)

This calculation shows that the 6.2 N net force is directed upwards, causing the rock to accelerate against the planet's gravity.