Question

The weight of an object in space is 500 N. Use ratios to obtain the objects new weight at:A. Half the distance from the centre of the EarthB. At 1/8 the distance from the centre of the EarthC. At 0.66 the distance from the centre of the Earth

Answer 1

To calculate the new weight of the object at different distances from the center of the Earth, you can use ratios. At half the distance, the weight is 125 N. At 1/8 the distance, the weight is 7.81 N. At 0.66 the distance, the weight is 217.8 N.

Step-by-step explanation:

To obtain the new weight of the object at different distances from the center of the Earth, we can use a ratio between the weights at the different distances. Let's calculate the new weights:

A. Half the distance from the center of the Earth: If the weight of the object in space is 500 N, then at half the distance from the center of the Earth, the new weight would be 1/4th of 500 N, which is 125 N.

B. At 1/8 the distance from the center of the Earth: If the weight of the object in space is 500 N, then at 1/8 the distance from the center of the Earth, the new weight would be 1/64th of 500 N, which is 7.81 N.

C. At 0.66 the distance from the center of the Earth: If the weight of the object in space is 500 N, then at 0.66 the distance from the center of the Earth, the new weight would be 0.4356 times 500 N, which is 217.8 N.

Answer 2

ANSWERS

A. 2000N

B. 32000N

C. 1147.8 N

EXPLANATION

In Newton's law of universal gravitation equation,

`F=G\cdot(m_1m_2)/(r^2)`

If we have the same two objects, but we change the distance between them, the factors G*m1*m2 remain constant,

`F\cdot r^2=Gm_1m_2=constant`

A. If the new distance, r2, is half the original distance of the object, r1, we have,

`F_1r^2_1=F_2r^2_2`

Knowing that r2 = 0.5r1, and that F1 is 500N, solve for F2,

`F_2=F_1\cdot(r^2_1)/(r^2_2)=500N\cdot(r^2_1)/((0.5)^2r^2_1)=500N\cdot(1)/(0.25)=2000N`

B. Now, we have to do the same but in this case, r2 = 1/8r1,

`F_2=F_1\cdot(r^2_1)/((1/8)^2r^2_1)=F_1\cdot8^2=500N\cdot64=32000N`

C. And finally, r2 = 0.66r1,

`F_2=F_1\cdot(r^2_1)/((0.66)^2r^2_1)=500N\cdot(1)/(0.4356)\approx1147.8N`