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Chapter 4: Q4CQ (page 159)
What is the relationship between weight and mass? Which is an intrinsic, unchanging property of a body?
Weight is the product of mass and force due to gravity. Mass is an intrinsic, unchanging property of the body.
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How are inertia and mass related?
Since astronauts in orbit are apparently weightless, a clever method of measuring their masses is needed to monitor their mass gains or losses to adjust diets. One way to do this is to exert a known force on an astronaut and measure the acceleration produced. Suppose a net external force of 50.0 N is exerted and the astronaut鈥檚 acceleration is measured to be 0.893 m/s2.
(a) Calculate her mass.
(b) By exerting a force on the astronaut, the vehicle in which they orbit experiences an equal and opposite force. Discuss how this would affect the measurement of the astronaut鈥檚 acceleration. Propose a method in which recoil of the vehicle is avoided.
If a constant, nonzero force is applied to an object, what can you say about the velocity and acceleration of the object?
A basketball player jumps straight up for a ball. To do this, he lowers his body 0.300 m and then accelerates through this distance by forcefully straightening his legs. This player leaves the floor with a vertical velocity sufficient to carry him 0.900 m above the floor.
(a) Calculate his velocity when he leaves the floor.
(b) Calculate his acceleration while he is straightening his legs. He goes from zero to the velocity found in part (a) in a distance of 0.300 m.
(c) Calculate the force he exerts on the floor to do this, given that his mass is 110 kg.
Unreasonable Results
(a) What is the initial acceleration of a rocket that has a mass of 1.50脳106 kg at takeoff, the engines of which produce a thrust of 2.00脳106 N ? Do not neglect gravity.
(b) What is unreasonable about the result? (This result has been unintentionally achieved by several real rockets.)
(c) Which premise is unreasonable, or which premises are inconsistent? (You may find it useful to compare this problem to the rocket problem earlier in this section.)
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