A gas fills the right portion of a horizontal cylinder whose radius is 5.33 cm. The initial pressure of the gas is 2.29 x 105 Pa. A frictionless movable piston separates the gas from the left portion of the cylinder that is evacuated and contains an ideal spring, as the drawing shows. The piston is initially held in place by a pin. The spring is initially unstrained, and the length of the gas-filled portion is 18.9 cm. When the pin is removed and the gas is allowed to expand, the length of the gas-filled chamber doubles. The initial and final temperatures are equal. Determine the spring constant of the spring.

What is the length x of the side of the triangle below? (hint: use the cosine function)

If the temperature were raised very high, classically what would we expect the heat capacity per object to be for this one-dimensional system? give a numerical value. chigh t = __ j/k/object (one reason for the discrepancy is that the high-temperature limit assumes that the number of oscillators is large (n > > 1), which is not the case in this tiny system.)

For problems 1-3, consider a simple dc brush motor with a permanent magnet stator. with an an consider a simple dc brush motor with a permanent magnet ae supply voltage of 100 v, the no-load speed of the motor is 1000 rpm. this motor can provide a torque of 1.9 n-m at 800 rpm drawing a current of 2 a current are both zero at no load.) 1. with an armature supply voltage of 100 v, the motor is operated at 900 rpm. what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input? what is the energy efficiency of the motor? with an armature supply voltage of 100 v, the motor is operated at 1100 rpm (where it acts as a generator). what torque input is required? what mechanical power is required what current is generated? what is the electrical power generated? what is the energy efficiency of the motor acting as a generator? 2. with an armature supply voltage raised to 120 v, the motor is operated at 1000 rpm. what is the no-load speed? what is the motor torque? what is the mechanical power delivered by the motor? what is the current draw? what is the electrical power input what is the energy efficiency of the motor? 3.