earths mass is 5.98x10^24 kg. if a 100 kg person is standing on the surface of the earth (d=6,470,000 m), what is the force of gravity between earth and the person?

Aspecial electronic sensor is embedded in the seat of a car that takes riders around a circular loop-the-loop ride at an amusement park. the sensor measures the magnitude of the normal force that the seat exerts on a rider. the loop-the-loop ride is in the vertical plane and its radius is 23 m. sitting on the seat before the ride starts, a rider is level and stationary, and the electronic sensor reads 740 n. at the top of the loop, the rider is upside down and moving, and the sensor reads 370 n. what is the speed of the rider at the top of the loop?

The scalar triple product computes the magnitude m of the moment of a force vector f about a specified line. it is m = (r × f) · n, where r is the position vector from the line to the point of application of the force and n is a unit vector in the direction of the line. use matlab to compute the magnitude m for the case where f = [12, −5, 4] n, r = [−3, 5, 2] m, and n = [6, 5, −7].

When a vertical beam of light passes through a transparent medium, the rate at which its intensity i decreases is proportional to i(t), where t represents the thickness of the medium (in feet). in clear seawater, the intensity 3 feet below the surface is 25% of the initial intensity i0 of the incident beam. what is the intensity of the beam "10" feet below the surface? (give your answer in terms of i0. round any constants or coefficients to five decimal places.)