Problem \"Biological motors) ATPase is a membrane protein that synthesizes ATP, the : energy currency of the cell. The protein acts as a rotary ! motor, making discrete 120 turns with each step while I producing one ATP. VI. F1 A. If 36 ATP are synthesized, how many.r rotations does the protein make? B. As shown in the figure, there are a and subu nits of the protein, rigidly affixed to its axis of rotation. lfthe B-subunits are 5.0 run away from the axis of rotation, what is the distance [in nm] traveled by the Bsubunits after two steps? Suppose Vlad and Rick are running against each other on a circular .- _____ track. They initially position themselves as shown in the figure, with {u- aux i i ' I Rick and Vlad 20 m and 23 m away from the track center, I!!!\" N i ' respectively. Assume their distances from the center are constant as i I: Rick ' Vlad they run; that is, they both run in circular paths. For questions A to E, '3'\" i; '4' assume they only complete one lap. '\\:\"--.__-.':d." A. What distance [in mi does Rick have to cover in one complete lap? B. What distance (in m) does Vlad have to cover in one complete lap? QUESTION 5 C. If we want to make this a fair race, we can have Vlad start ahead of Rick on the track and have both of them Vlad end at the same finish line (see figure). How far ahead (in m) must Vlad start for them to cover the same Finish line for both distance when travelling from their starting position to the finish line?Problem 4 [Three coins) 3 (cm) Three identical coins lie on three comers of a square 10.0 cm to ...._. on a side, as shown in the figure to the right. a. What is the x-coordinate of the center of mass of this system (in cm)? x [cm] QUESTION 10 b. What is the ycoordinate of the center of mass of this system [in cm)? A uniform rod of length 1.2 m and mass 3 kg has a small spherical ball of mass 1.5 kg attached to one end of the rod. The other end of the rod is joined to the wall by a hinge. A wire is attached to middle of the rod {at a distance of 0.6 rn from the hinge} and holds the rod in a horizontal position. The wire makes an angle of 40" with the horizontal. A. Where is the oenterofmass of the combined object consisting of the rod-plus-ball located as measured from the hinge? Give your answer in centimeters. B. What is the torque due to gravity on the combined object? Give your answer in S.l. units. Note: Take the hinge as the pivot, and use the usual sign convention 11+ is saunter-clockwise, and is clockwise}. The disk in a computer disk drive spins up from rest to a final angular speed of 5400 rpm in 2.00 s. It has a radius of 6 cm. A. What is the average angular acceleration of the disk? Express your answer in units of radfsz. B. If the angular acceleration is treated as constant, what is the magnitude of the centripetal acceleration at t = 1.5 s? Express your answer in S.I. units.Problem 7. Calculate the torques in each of the following diagrams, assuming the length of the rod is 4 meters, and the applied force has a magnitude of 100 N in each case. In all six cases, the pivot is at the point 0. \fA drawbridge is being held stationary. This drawbridge is 10 m long and has a mass of 270 kg. It is attached at its base to a stone wall with a hinge. The 2.0 m drawbridge is uniform, so its center of gravity is exactly at its (geometric) center. The drawbridge is being fixed by a chain attached 2.0 m from the end of 40 the bridge. At this instant, the drawbridge is at an angle of 30 above the horizontal. In this problem, give all torques relative to the point 30 where the drawbridge is attached to the wall. (Remember clockwise torques are negative) A. What is the torque due to the weight of the drawbridge? Provide your answer in units of N . m. QUESTION 26 B. What is the magnitude of the tension force in the chain? Provide your answer in units of N.\fShown. 35 N 28 N A. Calculate the net torque, where the pivot is at the center of the disk. 1350 12 cm 24 cm 18 N