Final answer:
The work done on the mass by the Earth's gravity while it moves downward 0.12 m is +0.102312 Joules. This is calculated using the mass of 0.087 kg, the acceleration due to gravity (9.8 m/s²), and the distance moved.
Step-by-step explanation:
To calculate the work done on the mass by the Earth, we use the work-energy principle. The work done by a force is equal to the force times the distance over which it acts when the force and the distance are in the same direction. In this case, the force is the weight of the mass, which is the force of gravity (weight = mass × gravity).
The gravitational force (weight) can be calculated using:
- Weight (W) = mass (m) × acceleration due to gravity (g)
With a mass (m) of 0.087 kg and acceleration due to gravity (g) of 9.8 m/s² (standard value on Earth's surface), the weight of the mass is:
W = 0.087 kg × 9.8 m/s² = 0.8526 N
The work done (Work) by the Earth's gravitational force as the mass moves downward can then be calculated using:
- Work (W) = force (F) × distance (d)
Here, the distance (d) the mass has moved is 0.12 m, so the work done by gravity is:
Work = 0.8526 N × 0.12 m = 0.102312 J
Since the force of gravity and the displacement are in the same direction, the work done by Earth's gravity is positive. Thus, the work done by Earth on the mass as it moves downward is +0.102312 Joules.