Chapter 6: Q.7 (page 153)
Are the following statements true or false? Explain.
a. The mass of an object depends on its location.
b. The weight of an object depends on its location.
c. Mass and weight describe the same thing in different units.
(a) It is untrue.
(b) It is correct.
(c) It is untrue.
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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, .
A rifle with a barrel length of cm fires a g bullet with a horizontal speed of m/s. The bullet strikes a block of wood and penetrates to a depth of cm.
a. What resistive force (assumed to be constant) does the wood exert on the bullet?
b. How long does it take the bullet to come to rest?
A ball tossed straight up has v = 0 at its highest point. Is it in equilibrium? Explain.
Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a “crumple zone” in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton’s first law!) until hitting the dashboard or windshield. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about . a. A person is in a head-on collision. The car’s speed at impact is . Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys.
b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag
A kg locomotive is traveling at when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop? Assume the track is level.
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