Find an exact expression for the magnitude of the tidal force applied by Earth to our rock of mass m
To find the magnitude of the tidal force applied by Earth to our rock of mass m, we need to understand the concept of tidal forces and the factors that contribute to their calculation.
Tidal forces result from the gravitational interaction between two bodies. In this case, Earth (considered as one body) exerts a gravitational force on our rock. The magnitude of this tidal force can be found using the formula:
F = (2GMmr)/(d^3)
where F is the magnitude of the tidal force, G is the gravitational constant (approximately 6.67430 × 10^-11 m^3⋅kg^-1⋅s^-2), M is the mass of Earth, m is the mass of the rock, and d is the distance between the center of Earth and the rock.
To calculate the tidal force, we need to determine the values for M, m, and d. The mass of Earth is approximately 5.972 × 10^24 kilograms. The mass of the rock, m, needs to be provided. The distance, d, should be measured from the center of Earth to the rock's location.
Once these values are known, you can plug them into the formula to calculate the magnitude of the tidal force.