91Ó°ÊÓ

Gravitational acceleration is a measure of how quickly an object speeds up when it is falling freely under gravity alone. This quantity varies depending on the celestial body you are on. Unlike Earth, other planets have different masses and radii, which influence their gravitational pull.
Gravitational acceleration can be derived from the weight of an object, as illustrated in this exercise. The weight of an object is the force exerted on it due to gravity, calculated by multiplying the mass of the object by the gravitational acceleration, using the formula:

• \( W = m \times g \)

Here, \( g \) represents the gravitational acceleration.
For the given problem, we know the weight of the rock is 40.0 N and the mass is 5.00 kg. By arranging the equation to solve for \( g \), we have:

• \( g = \frac{W}{m} = \frac{40.0 \; \mathrm{N}}{5.00 \; \mathrm{kg}} = 8.0 \; \mathrm{m/s^2} \)

This calculation informs us that the gravitational acceleration on the distant planet is 8.0 m/s², which is different from Earth's 9.81 m/s².

The concept of net force is crucial in understanding how objects move under various influences. Net force is essentially the sum of all forces acting on an object and determines how the object's motion changes.
In our example, the astronaut applies an upward force of 46.2 N to counteract the rock's weight. The weight acts downwards with a force of 40.0 N. To find the net force, we subtract the downward force (weight) from the upward force exerted by the astronaut:

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

The resulting net force of 6.2 N indicates that there is still an upward force acting on the rock after overcoming the planet's gravitational pull. This net force is responsible for the rock's acceleration.

Acceleration is the rate of change of velocity of an object when a net force is applied, as expressed in Newton's Second Law. This law is succinctly written as:

• \( F_{net} = m \times a \)

where \( F_{net} \) is the net force, \( m \) is the mass, and \( a \) is the acceleration we are looking to find.
In the present exercise, given the net force of 6.2 N and the rock's mass of 5.00 kg, we rearrange the formula to solve for acceleration:

• \( a = \frac{F_{net}}{m} = \frac{6.2 \; \mathrm{N}}{5.00 \; \mathrm{kg}} = 1.24 \; \mathrm{m/s^2} \)

This shows that the rock accelerates upwards at a rate of 1.24 m/s² when the astronaut applies a force of 46.2 N on the planet. It highlights how a net force results in a change in the rock's velocity.