If the block in Fig. 4.22 is released, it will over- come static friction and slide rapidly down the plane. What push P directed up the incline will re- tard the downward motion until the block moves at constant speed?

CASE STUDY In Example 34.6 (page 1111), we imagined equipping 1950DA, an asteroid on a collision course with the Earth, with a solar sail in hopes of ejecting it from the solar system. We found that the enormous size required for the solar sail makes the plan impossible at this time. Of course, there is no need to eject such an object from the solar system: we only need to change the orbit. A much more pressing problem is Apophis, a 300-m asteroid that may be on a collision course with the Earth and is due to come by on April 13, 2029. It is unlikely to hit the Earth on that pass, but it will return again in 2036. If Apophis passes through a 600-m keyhole on its 2029 pass, it is expected to hit the Earth in 2036. causing great damage. There are plans to deflect Apophis when it comes by in 2029. For example, we could hit it with a 10- to 150-kg impactor accelerated by a solar sail. The impactor is launched from the Earth to start orbiting the Sun in the same direction as the Earth and Apophis. The idea is to use a solar sail to accelerate the impactor so that it reverses direction and collides head-on with Apophis at 8090 km/s and thereby keeps Apophis out of the keyhole. Consider the momentum in the impactors orbit (Fig. P34.75) when the solar sail makes an angle of = 60 with the tangent to its orbit. Current solar sails may be about 40 m on a side, but the hope is to construct some that are about 160 m on a side. Estimate the impactors tangential acceleration when it is about 1 AU from the Sun. Keep in mind that the sail is neither a perfect absorber nor a perfect reflector, and a heavier impactor would presumably be equipped with a larger sail. Dont be surprised by what may seem like a very small acceleration. FIGURE P34.75

Show that, when SI units for 0 and 0 are entered, the units given by the right-hand side of the equation in the problem above are m/s.

You are a coach for the Physics Olympics team participating in a competition overseas. You are given the following sample problem to present to your team of students, which you need to solve very quickly: A person is standing on the midline of a soccer field. At one end of the field, as shown in Figure P24.28, is a letter D, consisting of a semicircular metallic ring of radius R and a long straight metal rod of length 2R, the diameter of the ring. The plane of the ring is perpendicular to the ground and perpendicular to the midline of the field shown by the broken line in Figure P24.28. Because of an approaching lightning storm, the semicircular ring and the rod become charged. The ring and the rod each attain a charge Q. What is the electric potential at point P, which is at a position x along the midline of the field, measured from the center of the rod, due to the letter D? Think quickly and use all resources available to you, which include your physics textbook: yon are in competition! Figure P24.28