Assignment Submission or this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer. Assignment Scoring Your last submission is used for your score. 1. [-/5 Points] DETAILS MY NO The graph below shows data taken on the position of a small massive cart attached to a spring as shown in the figure at the right. 5.0x (cm) . X Find the period (T), frequency (), and angular frequency (w) of the oscillation. T = S 1/s @ = rad/s B. If the spring constant is k = 2.5 N/m, can you find the mass of the cart? If you can do it, give the answer here. If you can't, put 0. m = kg The simple mass on a spring is the basis for our description of almost any oscillation. Let s consider the vibrational states of a simple diatomic molecule, say N2. We will model it as two identical masses connected by a spring as shown in the figure at the top right. This is a little different from the cart on a spring since there is no wall -- both of the atoms are moving. But if we only look at oscillations of the molecule where the center of mass is not moving, the atoms are moving equally and oppositely. When one is going left, the other atoms actually afrothe she went and vice versa. This is like two carts attached to a wall and oscillating equally and oppositely as shown in the lower picture. The only difference is difference is the way we treat the spring. When each atom moves a distance x, the spring betwoor ctually stretches a distance 2x, so the force on each atom is -2kx. We can ther We can therefore model the motion of one of the nitrogen atoms as a single cart on a spring if we replace k by 2k. C. If the angular frequency of oscillation of N2 is found to be 4.5 x 1018 rad/s, and the mass of a single nitrogen atom is 2.3 x 10-26 kg, find the effective spring constant between the two atoms. (Give your answer in Nm, since nanometers is a more appropriate scale for atoms than meters.) k = Nm 2. [14/14 Points] DETAILS PREVIOUS ANSWERS MY NOTES A mass hanging from a vertical spring is somewhat more complicated than a mass attached to a horizontal spring because the gravitational force acts along the direction of motion. Therefore, the restoring force of the oscillations is not provided by the spring force alone, but by the net force resulting from both the spring force and the gravitational force. Ultimately, however, the physical quantities of motion (position, velocity, and acceleration) for a vertical mass on a spring exhibit the same oscillations as a horizontal mass on a spring. 100 9 mass hangs from a vertical spring as shown in the picture. The measuring stick shows us the vertical y p cigshows us the vertical y position of the bottom of the spring with the origin (y = 0) at the top of the spring. Note that the positive y direction is downward. The 1 shown (y = 50 cm). The dashed line in the picture (y = 30 cm) indicates the unstretched resting length of the spring. The mass is pulled down 7 cm, stretching the bottom of the spring to y = 57 cm, and then released so that it begins oscillating mass is at rest at the position esc 20 DII DD F1 F3 F4 F5 F6 F7 F8 F9 F10 F11 F12 a # % &D. Calculate the current in each of the other two bulbs. B: 0.02 amps C: 0.04 amps 2. [1/7 Points] DETAILS PREVIOUS ANSWERS MY NOTES In the figure is shown another circuit that can be used to model a cell membrane. In this particular model, the plates of the capacitor (Inside the plastic shell shown in the picture) represent the Inside and outside of the membrane while the batteries represent different ion channels within the membrane. The opening of different ion channels is modeled by varying the resistances; these changes in the resistance then cause a change in the potential difference between the capacitor plates. For this problem, we will only consider fixed values for the resistances. All of the questions below refer to the circuit in its "steady state", meaning that the charge on the capacitor is constant and neither increasing nor decreasing. For each battery, use a potential difference of 5 V (the orange end is the high potential end). Resistor 1 is 13 2 and resistor 2 is 9 . The capacitor has a capacitance of 0.16 F. 1. What is the current flowing to the capacitor? Ic = 2. What is the current flowing through resistor 1 and what direction is it flowing? IR1 = A, upward x 3. What is the current flowing through resistor 2 and what direction is it flowing? IR2= A, upward 4. What is the potential difference (magnitude) across the capacitor? 5. What is the charge (magnitude) stored on each of the capacitor plates? 1Q1 = Submit Answer Submit Assignment Save Assignment Progress Home My Assignments DII DO FM1 F12 20 888 FB F9 F10 F5 F6 F7 esc 51 F3 F4 % A & @ # 18 9 2 3