Additional Problems

| 18 | A jetliner has a mass of 1.2 = 105 kg and flies at a speed of 140 m/s. (a) Find the magnitude of its momentum. (b) If the speed of light in a vacuum had the hypothetical value of 170 m/s, what would be the magnitude of the jetliner’s momentum?

| 19 | ssm A woman is 1.6 m tall and has a mass of 55 kg. She moves past an observer with the direction of the motion parallel to her height. The observer measures her relativistic momentum to have a magnitude of 2.0 × 1010 kg · m/s. What does the observer measure for her height?

| 20 | A spacecraft has a nonrelativistic (or classical) momentum whose magnitude is 1.3 × 1013 kg · m/s. The spacecraft moves at such a speed that the pilot measures the proper time interval between two events to be one-half the dilated time interval. Find the relativistic momentum of the spacecraft.

* | 21 | ssm An unstable particle is at rest and suddenly breaks up into two fragments. No external forces act on the particle or its fragments. One of the fragments has a velocity of +0.800c and a mass of 1.67 × 10−27 kg, and the other has a mass of 5.01 × 10−27 kg. What is the velocity of the more massive fragment? (Hint: This problem is similar to Example 6 in Chapter 7.)
Section 28.6 The Equivalence of Mass and Energy

| 22 | Radium is a radioactive element whose nucleus emits an α par ticle (a helium nucleus) with a kinetic energy of about 7.8 × 10−13 J (4.9 MeV). To what amount of mass is this energy equivalent?

| 23 | ssm Determine the ratio of the relativistic kinetic energy to the nonrelativistic kinetic energy () when a particle has a speed of (a) and (b) 0.970c.

| 24 | Suppose one gallon of gasoline produces of energy, and this energy is sufficient to operate a car for twenty miles. An as pirin tablet has a mass of 325 mg. If the aspirin could be converted completely into thermal energy, how many miles could the car go on a single tablet?

| 25 | Four kilograms of water are heated from 20.0 °C to 60.0 °C. (a) How much heat is required to produce this change in temperature? [The specific heat capacity of water is 4186 J/(kg · C°).] (b) By how much does the mass of the water increase?

| 26 | Multiple-Concept Example 6 reviews the principles that play a role in this problem. A nuclear power reactor generates of power. In one year, what is the change in the mass of the nuclear fuel due to the energy being taken from the reactor?

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