GO In Fig. 9-45a, a 4.5 kg dog stands on an 18 kg flatboat at dis- 0•17 Dog's displacement da tance D = 6.1 m from the shore. It walks 2.4 m along the boat toward shore and then stops. Assuming no friction between the boat and the wa- Boat's displacement d, ter, find how far the dog is then from the shore. (Hint: See Fig. 9-45b.) (b) Figure 9-45 Problem 17.

A carbon monoxide molecule lies along an x axis, with the carbon atom at x = 0 and the oxygen atom at x = 1.162 x 10 10 m. At what value of x is the molecule's center of mass located? Number Units

Radical Albertan separatists are driving a tank at a constant speed of 10 m/s up a 45 degree mountain slope, in a vain attempt to invade British Columbia. Pursued by the Mounties, the tank fires a 10 kg watermelon, with muzzle velocity 25 m/s, back along its path. Ignore the distance from the muzzle to the slope. If the gun barrel is pointed 20 degrees above the horizontal as shown, how far is the melon from the tank (which keeps moving) when it finally strikes the slope below? Answer in m.

52. The Center of Mass of Sulfur Dioxide Sulfur dioxide (SO₂) consists of two oxygen atoms (each of mass 16 u, where u is defined in Problem 40) and a single sulfur atom (of mass 32 u). The center-to-center distance between the sulfur atom and either of the oxygen atoms is 0.143 nm, and the angle formed by the three atoms is 120°, as shown in Figure 9-20. Find the x and y coordinates of the center of mass of this molecule. Oxygen 0.143 nm y 120° Oxygen 0.143 nm Sulfur A FIGURE 9-20 Problem 52 I

Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106°. If the bond length r= 0.110 nm long, locate the center of mass of the molecule. The mass m, of the hydrogen atom is 1.008 u, and the mass mo of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.) 53 nm YCH nm Submt Answer

Consider the schematic of the molecule shown, with two hydrogen atoms, H, bonded to an oxygen atom, O. The angle between the two bonds is 106°. If the bond length r = 0.099 nm long, locate the center of mass of the molecule. The mass m of the hydrogen atom is 1.008 u, and the mass mo of the oxygen atom is 15.9999 u. (Use a coordinate system centered in the oxygen atom, with the x-axis to the right and the y-axis upward. Give the coordinates of the center of mass in nm.) XCM Усм = = 0 H усм 53⁰ I = nm 53° Use trigonometry to determine the y-coordinate of the hydrogen molecules. Then apply the definition Σmyi Σmi nm r H

A water molecule consists of an oxygen atom with two hydrogen atoms bound to it (see the figure below). Suppose the angle between the two bonds is 104°. If the bonds are 0.0850 nm long, where is the center of mass of the molecule? (Take the origin to be the center of the oxygen atom and the x axis to be along the dotted line.) x = 0.00563 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. nm y = 0v nm 53 53 H. H

Molecules in a spherical container make wall collisions in a great circle plane of the sphere. All paths traveled between collisions are equal in length. (a) Relate the path length Al to the angle 0 and the sphere radius r. (b) Express the component of the molecular momentum transferred to the wall in a collision in terms of the molecular mass m, the speed v, and the angle 0. (c) Using parts (a) and (b), calculate the average force exerted on the wall by one molecule. (d) Derive the relation PV = PV = } Nmv² for a spheri- cal container. This is the same relation found for a rectangular box in Section 9.5.

A 130 lb person sitting in a 150 lb iceboat fires a gun, discharging a 2 oz bullet horizontally. If the bullet speed leaving the gun is 1200 ft/s, what will be the speed of the boat after the bullet is fired, if we assume no friction? The correct answer is 0.54 ft/s