Question

for the following questions use the gravitational force lab used with permission from phet interactive simulations, university of colorado boulder, http://phet.colorado.edu/gravitational force is the interaction between two masses. does it cause the masses to attract, repel or can it do either?which mass always experiences the greater force?how does increasing either mass affect the gravitational force?how does increasing the distance between masses affect the gravitational force?what is the magnitude of the force between a 350kg mass and a 600kg mass, spaced 7m apart?nyour answer will be very small. be careful with the number of zeroes!what is the greatest force that can be generated between the masses on the simulation (hint: be sure to check \constant size\)?nwhat is the least force, besides zero, that can be generated between the masses on the simulationnthe two problems below can be answered using extrapolation and have a 5% tolerance to allow for estimation. we recommend desmos graphing calculator to create graphs when necessary!what would be the magnitude of the force between a 250kg mass and a 1150kg mass, spaced 8m apart?nwhat would be the magnitude of the force between a 800kg mass and a 700kg mass, spaced 11m apart?nbased on what you have learned so far, answer this question! assume the masses of planets c & d are equal, and greater than the masses of a & b, which are also equal.

Explanation:

Step1: Recall gravitational force law

Newton's Law of Universal Gravitation: $F = G\frac{m_1m_2}{r^2}$, where $G = 6.674\times10^{-11}\ \text{N}\cdot\text{m}^2/\text{kg}^2$
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Conceptual Questions:

Step2: Gravitational force interaction

Gravitational force is always attractive.

Step3: Force magnitude and mass

By Newton's 3rd law, forces are equal.

Step4: Mass effect on force

Force is proportional to product of masses.

Step5: Distance effect on force

Force is inversely proportional to $r^2$.
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Calculation 1: 350kg & 600kg, 7m apart

Step6: Plug values into formula

$F = 6.674\times10^{-11}\times\frac{350\times600}{7^2}$

Step7: Compute numerator/denominator

$\frac{350\times600}{49} = \frac{210000}{49} \approx 4285.71$

Step8: Final force calculation

$F \approx 6.674\times10^{-11}\times4285.71 \approx 2.86\times10^{-7}$
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Simulation Force Limits (assume max mass=1000kg, min r=1m; min non-zero mass=1kg, max r=10m)

Step9: Max force calculation

$F_{max} = 6.674\times10^{-11}\times\frac{1000\times1000}{1^2} = 6.674\times10^{-5}$

Step10: Min non-zero force calculation

$F_{min} = 6.674\times10^{-11}\times\frac{1\times1}{10^2} = 6.674\times10^{-13}$
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250kg & 1150kg, 8m apart

Step11: Plug values into formula

$F = 6.674\times10^{-11}\times\frac{250\times1150}{8^2}$

Step12: Compute numerator/denominator

$\frac{250\times1150}{64} = \frac{287500}{64} \approx 4492.19$

Step13: Final force calculation

$F \approx 6.674\times10^{-11}\times4492.19 \approx 3.00\times10^{-7}$
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800kg & 700kg, 11m apart

Step14: Plug values into formula

$F = 6.674\times10^{-11}\times\frac{800\times700}{11^2}$

Step15: Compute numerator/denominator

$\frac{800\times700}{121} = \frac{560000}{121} \approx 4628.10$

Step16: Final force calculation

$F \approx 6.674\times10^{-11}\times4628.10 \approx 3.09\times10^{-7}$

Answer:

Conceptual Answers:

1. Gravitational force always causes masses to attract.
2. Both masses experience equal gravitational force.
3. Increasing either mass increases the gravitational force (force is directly proportional to the product of the masses).
4. Increasing the distance between masses decreases the gravitational force (force is inversely proportional to the square of the distance).

Numerical Answers:

1. Force between 350kg and 600kg (7m apart): $\boldsymbol{2.86\times10^{-7}\ \text{N}}$
2. Greatest force in simulation: $\boldsymbol{6.67\times10^{-5}\ \text{N}}$
3. Least non-zero force in simulation: $\boldsymbol{6.67\times10^{-13}\ \text{N}}$
4. Force between 250kg and 1150kg (8m apart): $\boldsymbol{3.00\times10^{-7}\ \text{N}}$
5. Force between 800kg and 700kg (11m apart): $\boldsymbol{3.09\times10^{-7}\ \text{N}}$