Section 1
Conceptual Questions
Suppose that the speed of a ball moving in a horizontal circle is increasing at a steady rate. Is this increase in speed produced by the centripetal acceleration? Explain.
A car travels around a curve with constant speed.a. Does the velocity of the car change in this process? Explain.b. Is the car accelerated? Explain.
Two cars travel around the same curve, one at twice the speed of the other. After traveling the same distance, which car, if either, has experienced the larger change in velocity? Explain.
A car travels the same distance at constant speed around two curves, one with twice the radius of curvature of the other. For which of these curves is the change in velocity of the car greater? Explain.
The centripetal acceleration depends on the square of the speed rather than just being proportional to the speed. Why does the speed enter twice? Explain.
A ball on the end of a string is whirled with constant speed in a counterclockwise, horizontal circle. At point A in the circle, the string breaks. Which of the curves sketched in the diagram most accurately represents the path that the ball will take after the string breaks (as seen from above)? Explain.
Before the string breaks in question 6 , is there a net force acting upon the ball? If so, what is its direction? Explain.
For a ball being twirled in a horizontal circle at the end of a string, does the vertical component of the force exerted by the string produce the centripetal acceleration of the ball? Explain.
A car travels around a flat (nonbanked) curve with constant speed.a. Sketch a diagram showing all of the forces acting upon the car.b. What is the direction of the net force acting upon the car? Explain.
Is there a maximum speed at which the car in question 9 will be page 99 able to negotiate the curve? If so, what factors determine this maximum speed? Explain.
If a curve is banked, is it possible for a car to negotiate the curve even when the frictional force is zero due to very slick ice? Explain.
If a ball is whirled in a vertical circle with constant speed, at what point in the circle, if any, is the tension in the string the greatest? Explain. (Hint: Compare this situation to the Ferris wheel described in section 5.2.)
Sketch the forces acting upon a rider on a Ferris wheel when the rider is at the top of the cycle, labeling each force clearly. Which force is largest at this point, and what is the direction of the net force? Explain.
Which safety measure, seat belts or air bags, offers the most protection in head-on collisions? Explain. (See everyday phenomenon box 5.1.)
In a head-on collision between two vehicles, is there a force that propels a driver forward toward the windshield? Explain. (See everyday phenomenon box 5.1.)
If a car is equipped with air bags, should it be necessary to also wear seat belts? Explain. (See everyday phenomenon box 5.1.)
In what way did the heliocentric view of the solar system proposed by Copernicus provide a simpler explanation of planetary motion than the geocentric view of Ptolemy? Explain.
Did Ptolemy's view of the solar system require motion of the Earth, rotational or otherwise? Explain.
Heliocentric models of the solar system (Copernican or Keplerian) require that the Earth rotate on its axis, producing surface speeds of roughly $1000 \mathrm{MPH}$. If this is the case, why do we not feel this tremendous speed? Explain.
How did Kepler's view of the solar system differ from that of Copernicus? Explain.
Consider the method of drawing an ellipse pictured in figure $5.15$. How would we modify this process to make the ellipse into a circle, which is a special case of an ellipse? Explain.
Does a planet moving in an elliptical orbit about the sun move fastest when it is farthest from the sun or when it is nearest to the sun? Explain by referring to one of Kepler's laws.
Does the sun exert a larger force on the Earth than that exerted on the sun by the Earth? Explain.
Is there a net force acting on the planet Earth? Explain.
Three equal masses are located as shown in the diagram. What is the direction of the net force acting upon $m_{2}$ ? Explain.
Two masses are separated by a distance r. If this distance is doubled, isthe force of interaction between the two masses doubled, halved, orchanged by some other amount? Explain
A painter depicts a portion of the night sky as shown in the diagrambelow, showing the stars and a crescent moon. Is this view possible?Explain.
At what times during the day or night would you expect the new moon torise and set? Explain.
At what times of the day or night does the half-moon rise or set? Explain.
Are we normally able to see the new moon? Explain.
During what phase of the moon can a solar eclipse occur? Explain.
A synchronous satellite is one that does not move relative to the surface of the Earth; it is always above the same location. Why does such a satellite not just fall straight down to the Earth? Explain.
Is Kepler's third law valid for artificial satellites orbiting about the Earth? Explain.
Since the Earth rotates on its axis once every 24 hours, why don't high tides occur exactly twice every 24 hours? Explain.
Why is there a high tide rather than a low tide when the moon is on the opposite side of the Earth from the ocean and the gravitational pull of the moon on the water is the weakest? Explain. (See everyday phenomenon box $5.2 .$ )
Would tides exist if the gravitational force did not depend on the distance between objects? Explain. (See everyday phenomenon box 5.2.)