Unformatted text preview: ese two
factors mean that the weight on the planet is 2/9 or 0.222 times your earth-weight.
10. (c) Newton’s law of gravitation gives the answer, provided that the distance between the
centers of the spheres is used for r (r = 0.50 m + 1.20 m + 0.80 m), rather than the distance
between the surfaces of the spheres.
11. (a) The answer follows directly from the fact that weight W is given by W = mg, where m is
the mass and g is the acceleration due to the earth’s gravity. Thus, m = (784 N)/(9.80 m/s2) =
80.0 kg. The mass is the same on Mercury as on Earth, because mass is an intrinsic property
12. (d) What matters is the direction of the elevator’s acceleration. When the acceleration is
upward, the apparent weight is greater than the true weight. When the acceleration is
downward, the apparent weight is less than the true weight. In both possibilities the
acceleration points upward.
13. (b) According to Newton’s third law, the pusher and the wall exert forces of equal
magnitude but opposite directions on each other. The normal force is the component of the
wall’s force that is perpendicular to the wall. Thus, it has the same magnitude as the
component of the pusher’s force that is perpendicular to the wall. As a result, the normal
forces are ranked in the same order as the perpendicular components of the pusher’s forces.
The smallest perpendicular component is in B, and the largest is in C.
14. (a) The static frictional force is balancing the component of the block’s weight that points
down the slope of the incline. This component is smallest in B and greatest in A.
15. (b) The static frictional force that blocks A and B exert on each other has a magnitude f.
The force that B exerts on A is directed to the right (the positive direction), while the force
that A exerts on B is directed to the left. Blocks B and C also exert static frictional forces on
each other, but these forces have a magnitude 2f, because the normal force pressing B and C
together is twice the normal force pressing A and B together. The force that C exerts on B is
directed to the right, while the force that B exerts on C is directed to the left. In summary,
then, block A experiences a single frictional force +f, which is the net frictional force; block
B experiences two frictional forces, −f and +2f, the net frictional force being −f +2f = +f;
block C experiences a single frictional force +2f, which is the net frictional force. It follows
that fs, A = fs, B = fs, C/2.
16. (c) The magnitude of the kinetic frictional force is proportional to the magnitude of the
normal force. The normal force is smallest in B, because the vertical component of F
compensates for part of the block’s weight. In contrast, the normal force is greatest in C,
because the vertical component of F adds to the weight of the block. Chapter 4 Answers to Focus on Concepts Questions 161 17. (d) Acceleration is inversely proportional to mass, according to Newton’s second law. This
law also indicates that acceleration is directly proportional to the net force. The frictional
force is the net force acting on a block, and its magnitude is directly proportional to the
magnitude of the normal force. However, in each of the pictures the normal force is directly
proportional to the weight and, thus, the mass of a block. The inverse proportionality of the
acceleration to mass and the direct proportionality of the net force to mass offset each other.
The result is that the deceleration is the same in each case.
18. (e) In B the tension T is the smallest, because three rope segments support the weight W of
the block, with the result that 3T = W, or T = W/3. In A the tension is the greatest, because
only one rope segment supports the weight of the block, with the result that T = W.
19. (c) Since the engines are shut down and since nothing is nearby to exert a force, the net
force acting on the probe is zero, and its acceleration must be zero, according to Newton’s
second law. With zero acceleration the probe is in equilibrium.
20. (a) The hallmark of an object in equilibrium is that it has no acceleration. Therefore, an
object in equilibrium need not be at rest. It can be moving with a constant velocity.
21. (b) Since the object is not in equilibrium, it must be accelerating. Newton’s second law, in
turn, implies that a net force must be present to cause the acceleration. Whether the net
forces arises from a single force, two perpendicular forces, or three forces is not important,
because only the net force appears in the second law.
22. (d) The block is at rest and, therefore, in equilibrium. According to Newton’s second law,
then, the net force acting on the block in a direction parallel to the inclined surface of the
incline must be zero. This means that the force of static friction directed up the incline must
balance the component of the block’s weight directed down the incline
[(8.0 kg)(9.8 m/s2) sin 22º = 29 N].
23. (b) Since the boxes move at a constant velocity, they have no ac...
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