Question

Let’s drill a straight tunnel through the earth. It turns out that if an object of mass m is in the tunnel, a distance x from the center of the tunnel, then the gravitational and normal forces wild combine to exert a force on it of mgx/R toward the center of the tunnel – just as if the object were connected to the center of the tunnel by a spring. (Here g is the usual 9.8 m/s2 and R is the radius of the earth, 6.4×106 m.)(a) [10 pts.] Suppose the tunnel goes from Philadelphia, PA to Philadelphia, NY, a tunnel length of 600 km. If we drop a car in at one end of the tunnel, starting at rest, how long would it take the car to get to the other end of the tunnel? Please give your answer in minutes. (Assume there is no friction or air resistance!)(b) [7 pts.] What would the car’s greatest speed be (in meters per second, please), and where would it be when it has that speed? Would air resistance be an important force?(c) [3 pts.] How long would it take a similar car to roll through a straight tunnel from Philadelphia, PA to Philadelphia, MS, a distance of 1400 km?

Answer 1