Question
A student attempts to measure the maximum possible distance two masses can be away from one another and still register on the force-meter available. The masses are 2 kg and 7 kg respectively while the force-meter is capable of detecting a force as low as 0.000002 N. What is the greatest distance the masses can be apart and still register on the force-meter
Answers
Answered by
GPT 3.5
To determine the maximum distance the masses can be apart and still register on the force-meter, we need to calculate the gravitational force between the two masses and compare it to the minimum detectable force of the force-meter.
The gravitational force between two masses is given by the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 × 10^(-11) N m^2 / kg^2), m1 and m2 are the masses, and r is the distance between the masses.
We want to find the maximum distance, so we need to solve the equation for r:
r^2 = G * (m1 * m2) / F
r = sqrt(G * (m1 * m2) / F)
Given that m1 = 2 kg, m2 = 7 kg, and F = 0.000002 N, we can substitute these values into the equation:
r = sqrt((6.67 × 10^(-11) N m^2 / kg^2) * (2 kg * 7 kg) / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2 / kg^2) * 14 kg^2 / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2) * 14 kg^2 / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2) * 14 kg^2) / sqrt(0.000002 N)
r = (sqrt(93.38 × 10^(-11) N m^2 kg^2)) / sqrt(0.000002 N)
Simplifying further:
r ≈ (305.32 × 10^(-11) N m^2 kg) / (4.47 × 10^(-4) N)
r ≈ 0.683 m
Therefore, the greatest distance the masses can be apart and still register on the force-meter is approximately 0.683 meters.
The gravitational force between two masses is given by the equation:
F = G * (m1 * m2) / r^2
where F is the gravitational force, G is the gravitational constant (approximately 6.67 × 10^(-11) N m^2 / kg^2), m1 and m2 are the masses, and r is the distance between the masses.
We want to find the maximum distance, so we need to solve the equation for r:
r^2 = G * (m1 * m2) / F
r = sqrt(G * (m1 * m2) / F)
Given that m1 = 2 kg, m2 = 7 kg, and F = 0.000002 N, we can substitute these values into the equation:
r = sqrt((6.67 × 10^(-11) N m^2 / kg^2) * (2 kg * 7 kg) / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2 / kg^2) * 14 kg^2 / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2) * 14 kg^2 / (0.000002 N))
r = sqrt((6.67 × 10^(-11) N m^2) * 14 kg^2) / sqrt(0.000002 N)
r = (sqrt(93.38 × 10^(-11) N m^2 kg^2)) / sqrt(0.000002 N)
Simplifying further:
r ≈ (305.32 × 10^(-11) N m^2 kg) / (4.47 × 10^(-4) N)
r ≈ 0.683 m
Therefore, the greatest distance the masses can be apart and still register on the force-meter is approximately 0.683 meters.