QuestionCalculate the new gravitational force when two objects, initially 1000 N apart at distance D, are separated by D/4.

Studdy Solution

STEP 1

Assumptions1. The initial force between the two objects is1000 N. The initial distance between the two objects is D3. The force of gravity between two objects is calculated using the equation $=G \frac{m_{1} m_{}}{r^{}}$
4. The force is inversely proportional to the square of the distance between the two objects5. The masses of the objects and the gravitational constant do not change

STEP 2

First, let's write down the initial condition using the formula for gravitational force.
$_{1} = G \frac{m_{1} m_{2}}{^{2}}$

STEP 3

We know that the initial force $_{1}$ is1000 N. Let's substitute this value into the equation.
$1000 = G \frac{m_{1} m_{2}}{^{2}}$

STEP 4

Now, let's write down the equation for the new force when the distance between the objects is $/4$ .
$_{2} = G \frac{m_{1} m_{2}}{( /4)^{2}}$

STEP 5

implify the denominator in the equation for $_{2}$ .
$_{2} = G \frac{m_{1} m_{2}}{^{2} /16}$

STEP 6

Rearrange the equation for $_{2}$ to make it clearer.
$_{2} =16 \cdot G \frac{m_{1} m_{2}}{^{2}}$

STEP 7

We know that $G \frac{m_{1} m_{2}}{^{2}}$ is equal to1000 N from our initial condition. Let's substitute this into the equation for $_{2}$ .
$_{2} =16 \cdot1000$

STEP 8

Calculate the new force $_{2}$ .
$_{2} =16 \cdot1000 =16000 \, N$ The force between the two objects when they are separated by a distance of $/4$ is16000 N.

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QuestionCalculate the new gravitational force when two objects, initially 1000 N apart at distance D, are separated by D/4.

Studdy Solution

STEP 1

STEP 2

First, let's write down the initial condition using the formula for gravitational force.
$_{1} = G \frac{m_{1} m_{2}}{^{2}}$

STEP 3

We know that the initial force $_{1}$ is1000 N. Let's substitute this value into the equation.
$1000 = G \frac{m_{1} m_{2}}{^{2}}$

STEP 4

Now, let's write down the equation for the new force when the distance between the objects is $/4$ .
$_{2} = G \frac{m_{1} m_{2}}{( /4)^{2}}$

STEP 5

implify the denominator in the equation for $_{2}$ .
$_{2} = G \frac{m_{1} m_{2}}{^{2} /16}$

STEP 6

Rearrange the equation for $_{2}$ to make it clearer.
$_{2} =16 \cdot G \frac{m_{1} m_{2}}{^{2}}$

STEP 7

We know that $G \frac{m_{1} m_{2}}{^{2}}$ is equal to1000 N from our initial condition. Let's substitute this into the equation for $_{2}$ .
$_{2} =16 \cdot1000$

STEP 8

Calculate the new force $_{2}$ .
$_{2} =16 \cdot1000 =16000 \, N$ The force between the two objects when they are separated by a distance of $/4$ is16000 N.

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QuestionCalculate the new gravitational force when two objects, initially 1000 N apart at distance D, are separated by D/4.

Studdy Solution

STEP 1

STEP 2

First, let's write down the initial condition using the formula for gravitational force.1=Gm1m22_{1} = G \frac{m_{1} m_{2}}{^{2}}1​=G2m1​m2​​

STEP 3

We know that the initial force 1_{1}1​ is1000 N. Let's substitute this value into the equation.1000=Gm1m221000 = G \frac{m_{1} m_{2}}{^{2}}1000=G2m1​m2​​

STEP 4

Now, let's write down the equation for the new force when the distance between the objects is /4 /4/4.2=Gm1m2(/4)2_{2} = G \frac{m_{1} m_{2}}{( /4)^{2}}2​=G(/4)2m1​m2​​

STEP 5

implify the denominator in the equation for 2_{2}2​.2=Gm1m22/16_{2} = G \frac{m_{1} m_{2}}{^{2} /16}2​=G2/16m1​m2​​

STEP 6

Rearrange the equation for 2_{2}2​ to make it clearer.2=16⋅Gm1m22_{2} =16 \cdot G \frac{m_{1} m_{2}}{^{2}}2​=16⋅G2m1​m2​​

STEP 7

We know that Gm1m22G \frac{m_{1} m_{2}}{^{2}}G2m1​m2​​ is equal to1000 N from our initial condition. Let's substitute this into the equation for 2_{2}2​.2=16⋅1000_{2} =16 \cdot10002​=16⋅1000

STEP 8

Calculate the new force 2_{2}2​.2=16⋅1000=16000 N_{2} =16 \cdot1000 =16000 \, N2​=16⋅1000=16000NThe force between the two objects when they are separated by a distance of /4 /4/4 is16000 N.

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First, let's write down the initial condition using the formula for gravitational force.
$_{1} = G \frac{m_{1} m_{2}}{^{2}}$

We know that the initial force $_{1}$ is1000 N. Let's substitute this value into the equation.
$1000 = G \frac{m_{1} m_{2}}{^{2}}$

Now, let's write down the equation for the new force when the distance between the objects is $/4$ .
$_{2} = G \frac{m_{1} m_{2}}{( /4)^{2}}$

implify the denominator in the equation for $_{2}$ .
$_{2} = G \frac{m_{1} m_{2}}{^{2} /16}$

Rearrange the equation for $_{2}$ to make it clearer.
$_{2} =16 \cdot G \frac{m_{1} m_{2}}{^{2}}$

We know that $G \frac{m_{1} m_{2}}{^{2}}$ is equal to1000 N from our initial condition. Let's substitute this into the equation for $_{2}$ .
$_{2} =16 \cdot1000$

Calculate the new force $_{2}$ .
$_{2} =16 \cdot1000 =16000 \, N$ The force between the two objects when they are separated by a distance of $/4$ is16000 N.