The (in)famous Dr. Abner Malllity has a problem.  In his consulting work, the company has been working on a new force sensor.  It works in a way that the resistance changes as the applied force changes.  Dr. Mallity has used one in the voltage divider circuit below, and he has made the following measurements.

• When the force is zero, the resistance of the sensor is 1000W.  (i.e. one thousand ohms)
• When the force is 100 newtons, the resistance of the sensor is 2000W.
• In the circuit below, the voltage is measured across the sensor, and R_a is chosen as 1000W.  The supply voltage is 12 volts.

• What is the applied force when the measured output voltage is 6v?
• What is the applied force when the measured output voltage is 5v?