Get detailed and accurate responses to your questions on IDNLearn.com. Join our knowledgeable community and get detailed, reliable answers to all your questions.
Sagot :
To determine the new gravitational force between the Earth and the satellite when the distance is increased by a factor of 4, follow these steps:
1. Understand the gravitational force law:
The gravitational force between two masses is inversely proportional to the square of the distance between them. This means if the distance is [tex]\( d \)[/tex], the gravitational force [tex]\( F \)[/tex] is proportional to [tex]\( \frac{1}{d^2} \)[/tex].
2. Original force and distance information:
The original gravitational force between the Earth and the satellite is 243 N, at some initial distance [tex]\( d \)[/tex].
3. Effect of increasing the distance by a factor of 4:
If the distance increases to 4 times the original distance (i.e., [tex]\( 4d \)[/tex]), then according to the inverse square law, the force will be reduced by a factor of [tex]\( (4)^2 \)[/tex].
4. Calculate the factor reduction:
[tex]\[ \text{Reduction factor} = 4^2 = 16 \][/tex]
5. Determine the new force:
The new force is obtained by dividing the original force by this factor:
[tex]\[ \text{New Force} = \frac{\text{Original Force}}{\text{Reduction Factor}} = \frac{243}{16} \][/tex]
6. Perform the division to find the precise force:
[tex]\[ \text{New Force} = \frac{243}{16} \approx 15.1875 \][/tex]
7. Round the result to the nearest whole number:
We round 15.1875 to the nearest whole number, which gives 15.
Conclusion:
The new gravitational force between the Earth and the satellite, when it is moved to 4 times the original distance, is approximately [tex]\( 15 \)[/tex] N.
1. Understand the gravitational force law:
The gravitational force between two masses is inversely proportional to the square of the distance between them. This means if the distance is [tex]\( d \)[/tex], the gravitational force [tex]\( F \)[/tex] is proportional to [tex]\( \frac{1}{d^2} \)[/tex].
2. Original force and distance information:
The original gravitational force between the Earth and the satellite is 243 N, at some initial distance [tex]\( d \)[/tex].
3. Effect of increasing the distance by a factor of 4:
If the distance increases to 4 times the original distance (i.e., [tex]\( 4d \)[/tex]), then according to the inverse square law, the force will be reduced by a factor of [tex]\( (4)^2 \)[/tex].
4. Calculate the factor reduction:
[tex]\[ \text{Reduction factor} = 4^2 = 16 \][/tex]
5. Determine the new force:
The new force is obtained by dividing the original force by this factor:
[tex]\[ \text{New Force} = \frac{\text{Original Force}}{\text{Reduction Factor}} = \frac{243}{16} \][/tex]
6. Perform the division to find the precise force:
[tex]\[ \text{New Force} = \frac{243}{16} \approx 15.1875 \][/tex]
7. Round the result to the nearest whole number:
We round 15.1875 to the nearest whole number, which gives 15.
Conclusion:
The new gravitational force between the Earth and the satellite, when it is moved to 4 times the original distance, is approximately [tex]\( 15 \)[/tex] N.
Thank you for joining our conversation. Don't hesitate to return anytime to find answers to your questions. Let's continue sharing knowledge and experiences! Thank you for visiting IDNLearn.com. For reliable answers to all your questions, please visit us again soon.