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Chapter 6: Q.39 (page 156)
The 1000 kg steel beam is supported by two ropes. What is the tension in each?
Tension in rope 1 is
Tension in rope 2 is
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Large objects have inertia and tend to keep moving-Newton's BI0 first law. Life is very different for small microorganisms that swim through water. For them, drag forces are so large that they instantly stop, without coasting, if they cease their swimming motion. To swim at constant speed, they must exert a constant propulsion force by rotating corkscrew-like flagella or beating hair-like cilia. The quadratic model of drag of Equation fails for very small particles. Instead, a small object moving in liquid experiences a linear drag force, , the direction opposite the motion), where is a constant. For a sphere of radius , the drag constant can be shown to be , where is the viscosity of the liquid. Water at has viscosity .
a. A paramecium is about long. If it's modeled as a sphere, how much propulsion force must it exert to swim at a typical speed of ? How about the propulsion force of a --diameter . coli bacterium swimming at ?
b. The propulsion forces are very small, but so are the organisms. To judge whether the propulsion force is large or small relative to the organism, compute the acceleration that the propulsion force could give each organism if there were no drag. The density of both organisms is the same as that of water, .
The three ropes inare tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are and , the magnitudes of the tension forces in the first two ropes?
Astronauts in space "weigh" themselves by oscillating on a CALC spring. Suppose the position of an oscillating astronaut is given by, where is in . What force does the spring exert on the astronaut at
(a) and
(b) ? Note that the angle of the sine function is in radians.
A block pushed along the floor with velocity slides a distance d after the pushing force is removed.
a. If the mass of the block is doubled but its initial velocity is not changed, what distance does the block slide before stopping?
b. If the initial velocity is doubled to but the mass is not changed, what distance does the block slide before stopping?
Kat, Matt, and Nat are arguing about why a physics book on a table doesn鈥檛 fall. According to Kat, 鈥淕ravity pulls down on it, but the table is in the way so it can鈥檛 fall.鈥� 鈥淣onsense,鈥� says Matt. 鈥淎n upward force simply overcomes the downward force to prevent it from falling.鈥� 鈥淏ut what about Newton鈥檚 first law?鈥� counters Nat. 鈥淚t鈥檚 not moving, so there can鈥檛 be any forces acting on it.鈥� None of the statements is exactly correct. Who comes closest, and how would you change his or her statement to make it correct?
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