76. at Liftoff, the Saturn V Rocket Used for the Apollo Missions Has a Mass Of2.45 X 106 Kg

CHAPTER 6 REVIEW PROBLEMS

76. At liftoff, the Saturn V rocket used for the Apollo missions has a mass of2.45 X 106 kg.

(a) What is the minimum thrust that the rocket engines must develop to achieve liftoff?

(b) The actual thrust that the engines develop is 3.3 X 107 N. What is the vertical acceleration of the rocket at liftoff?

(c) At burnout, the rocket has spent its fuel, and its remaining
mass is 0.75 X 106 kg. What is the acceleration just before
burnout? Assume that the motion is still vertical and that
the strength of gravity is the same as when the rocket is on
the ground.

77. If the coefficient of static friction between the tires of an
automobile and the road is µs = 0.80, what is the minimum
distance the automobile needs in order to stop without skid-
ding from an initial speed of 90 km/h? How long does it take
to stop?

78. Suppose that the last car of a train becomes uncoupled-while
the train is moving upward on a slope of1:6 at a speed of 48 km/h.

(a) What is the deceleration of the car? Ignore friction.

(b) How far does the car coast up the slope before it stops?

79. A 40-kg crate falls off a truck traveling at 80 km/h on a level
road. The crate slides along the road and gradually comes to a
halt. The coefficient of kinetic friction between the crate and
the road is 0.80.

(a) Draw a "free-body" diagram for the crate sliding on the road.

(b) What is the normal force the road exerts on the crate?
(c) What is the friction force the road exerts on the crate?
(d) What is the weight force on the crate? What is the net force on the crate?

(e) What is the deceleration of the crate? How far does the
crate slide before coming to a halt?

80. A 2.0-kg box rests on an inclined plane which makes an angle
of 30° with the horizontal. The coefficient of static friction
between the box and the plane is 0.90.

(a) Draw a "free-body" diagram for the box.

(b) What is the normal force the inclined plane exerts on
the box?

(d) What is the net force the inclined plane exerts on the box? What is the direction of this force?

81. The body of an automobile is held above the axles of the
wheels by means of four springs, one near each wheel. Assume that the springs are vertical and that the forces on all the springs are the same. The mass of the body of the automobile is 1200 kg, and the spring constant of each spring is 2.0 X 104 N/m. When the automobile is stationary on a level road, how far are the springs compressed from their relaxed length?

82. A block of wood rests on a sheet of paper lying on a table. The coefficient of static friction between the block and the
paper is µs = 0.70, and that between the paper and the table is µs = 0.50. If you tilt the table, at what angle will the block
begin to move?

83. Two blocks of masses m1 and m2 are connected by a string. One block slides on a table, and the other hangs from the string, which passes over a pulley (see Fig. 6.46). The coefficient of sliding friction between the first block and the table is µs = 0.20. What is the acceleration of the blocks?

FIGURE 6.4 Mass on table, pulley, and hanging mass

*84. A man of mass 75 kg is pushing a heavy box on a flat floor. The coefficient of sliding friction between the floor and the box is 0.20, and the coefficient of static friction between the man's shoes and the floor is 0.80. If the man pushes horizontally (see Fig. 6.47), what is the maximum mass of the box he can move?

FIGURE 6.47 Pushing a box

85. Two springs of constants 2.0 x 103 N/m and 3.0 x 103 N/m are connected in tandem, a mass of 5.0 kg hangs vertically from the bottom of the lower spring. By what amount does the mass stretch the combined spring? Each individual spring?

86. A block of mass 1.5 kg is placed on a flat surface, and it is
being pulled horizontally by a spring with a spring constant
1.2 X 103 N/m (see Fig. 6.48). The coefficient of static friction
between the block and the table is µs = 0.60, and the coefficient of sliding friction is µk = 0.40.

(a) By what amount must the spring be stretched to start the block moving?

(b) What is the acceleration of the block if the stretch of the
spring is maintained at a constant value equal to that
required to start the motion?

FIGURE 6.48 Mass pulled by spring.

87. A block of mass 1.5 kg is placed on a plane inclined at 30°, and
it is being pulled upward by a spring with a spring constant
1.2 X 103 N/m (see Fig. 6.49). The direction of pull of the
spring is parallel to the inclined plane. The coefficient of static
friction between the block and the inclined plane is µs = 0.60,
and the coefficient of sliding friction is µk = 0.40.

(a) By what amount must the spring be stretched to start the
block moving?

(b) What is the acceleration of the block if the stretch of the
spring is maintained at a constant value equal to that
required to start the motion?

FIGURE 6.49 Block on incline pulled by spring.

88. A mass m1 slides on a smooth, frictionless table. The mass is
constrained to move in a circle by a string that passes through
a hole in the center of the table and is attached to a second
mass m2 hanging vertically below the table (Fig. 6.50). If the radius of the circular motion of the first mass is r, what must be its speed?

FIGURE 6.50 Mass in circular motion and hanging mass.

89. An automobile enters a curve of radius 45 m at 70 km/h. Will
the automobile skid? The curve is not banked, and the coefficient of static friction between the wheels and the road is 0.80.

90. A stone of 0.90 kg attached to a rod is being whirled around
a vertical circle of radius 0.92 m. Assume that during this
motion the speed of the stone is constant. If at the top of the
circle the tension in the rod is (just about) zero, what is the
tension in the rod at the bottom of the circle?