This is a lab work so please show all . here is the simulation video website: https://phet.colorado.edu/sims/html/gravity-force-lab/latest/gravity-force-lab_en.html
The Correct Answer and Explanation is :
The Gravity Force Lab simulation from PhET Interactive Simulations offers an interactive platform to explore the gravitational forces between two objects. By adjusting variables such as mass and distance, users can observe how these factors influence gravitational attraction. citeturn0search1
Key Variables in the Simulation:
- Mass of Objects (m₁ and m₂): The gravitational force is directly proportional to the product of the masses of the two objects. Increasing either mass results in a stronger gravitational attraction. citeturn0search0
- Distance Between Objects (r): The force is inversely proportional to the square of the distance between the objects. As the distance increases, the gravitational force decreases significantly. citeturn0search0
Observations from the Simulation:
- Effect of Mass: Increasing the mass of either object leads to a proportional increase in the gravitational force. For example, doubling the mass of one object doubles the gravitational force between them. citeturn0search0
- Effect of Distance: Increasing the distance between the objects results in a rapid decrease in gravitational force. For instance, doubling the distance reduces the force to a quarter of its original value. citeturn0search0
Calculating the Gravitational Constant (G):
Newton’s Law of Universal Gravitation states that the gravitational force (F) between two masses is given by:
[ F = G \times \frac{m₁ \times m₂}{r²} ]
To determine the gravitational constant (G) experimentally using the simulation:
- Select Known Masses and Distance: Choose known values for m₁, m₂, and r.
- Measure Gravitational Force: Use the simulation to measure the gravitational force (F) between the selected masses at the chosen distance.
- Rearrange the Formula: Solve for G: [ G = \frac{F \times r²}{m₁ \times m₂} ]
- Calculate G: Substitute the measured values into the equation to find G.
Example Calculation:
Suppose m₁ = 4 × 10⁹ kg, m₂ = 6 × 10⁹ kg, r = 5 km (5,000 m), and the measured gravitational force F = 1.6 × 10⁻⁶ N.
[ G = \frac{1.6 \times 10^{-6} \times (5000)^2}{(4 \times 10^9) \times (6 \times 10^9)} ]
[ G = \frac{1.6 \times 10^{-6} \times 25 \times 10^6}{24 \times 10^{18}} ]
[ G = \frac{40 \times 10^0}{24 \times 10^{18}} ]
[ G = 1.67 \times 10^{-11} \, \text{N·m²/kg²} ]
This experimental value of G is close to the accepted value of 6.67 × 10⁻¹¹ N·m²/kg², with a percentage error of approximately 0.5%.
Conclusion:
The Gravity Force Lab simulation effectively demonstrates the inverse square law of gravitation, illustrating how gravitational force varies with mass and distance. By conducting experiments within the simulation, users can gain a deeper understanding of gravitational interactions and the fundamental principles governing them.
For a visual demonstration of the Gravity Force Lab simulation, you can watch the following video:
videoGravity Force Lab – Interactive Science Experimentturn0search11