Chapter 12, Problem 14RQ

1. 14. The data shown in the following graph was collected during testing of an electromagnetic mass driver. The energy to energize the electromagnets was obtained from a bank of capacitors. The capacitor bank was charged to various voltages, and for each voltage, the exit velocity of the projectile was measured when the mass driver was activated.

• Note

  Due to several complicated nonlinear losses in the system that are far beyond the

  scope of this course, this is a case of a power model in which the exponent does not come out to be an integer or simple fraction, so rounding to two significant figures is appropriate. In fact, this model is only a first approximation-a really accurate model would be considerably more complicated.

• 1. a. What would the velocity be if the capacitors were charged to 100,000 volts?
  2. b. What voltage would be necessary to accelerate the projectile to 1000 meters per second?
  3. c. Assume that the total capacitance is 5 farads. If the capacitors are initially charged to 10,000 volts and are discharged to 2000 volts during the launch of a projectile, what is the mass of the projectile if the overall conversion of energy stored in the capacitors to kinetic energy in the projectile has an efficiency of 20%? Recall that the energy stored in a capacitor is given by E = 0.5 CV², where C is capacitance in farads and V is voltage in volts.