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PROBLEM 12.24
An airplane has a mass of 25 Mg and its engines develop a total thrust of 40 kN during take-off. If the drag
D exerted on the plane has a magnitude
2
2.25 ,Dv=
where v is expressed in meters per second and D in
newtons, and if the plane becomes airborne at a speed of 240 km/h, determine the length of runway required
for the plane to take off.
SOLUTION
3 23
1
PROBLEM 12.25
A 4-kg projectile is fired vertically with an initial velocity of 90 m/s, reaches a maximum height and falls to
the ground. The aerodynamic drag D has a magnitude D = 0.0024
2
v
where D and v are expressed in newtons
and m/s, respectively. Knowing that the direction of the drag is always opposite to the direction of the
velocity, determine (a) the maximum height of the trajectory, (b) the speed of the projectile when it reaches
the ground.
SOLUTION
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 12.25 (Continued)
f
PROBLEM 12.26
A constant force P is applied to a piston and rod of total mass m to
make them move in a cylinder filled with oil. As the piston moves, the
oil is forced through orifices in the piston and exerts on the piston a
force of magnitude kv in a direction opposite to the motion of the
piston. Knowing that the piston starts from rest at
0t=
and
0,x=
show that the equation relating x, v, and t, where x is the distance
traveled by the piston and v is the speed of the piston, is linear in each
of these variables.
SOLUTION
PROBLEM 12.27
A spring AB of constant k is attached to a support at A and to a
collar of mass m. The unstretched length of the spring is
.
Knowing that the collar is released from rest at
0
xx=
and
neglecting friction between the collar and the horizontal rod,
determine the magnitude of the velocity of the collar as it passes
through Point C.
SOLUTION
Choose the origin at Point C and let x be positive to the right. Then x is a position coordinate of the slider B
and
0
x
is its initial value. Let L be the stretched length of the spring. Then, from the right triangle
22
0
m
PROBLEM 12.28
Block A has a mass of 10 kg, and blocks B and C have masses of 5 kg each.
Knowing that the blocks are initially at rest and that B moves through 3 m in 2 s,
determine (a) the magnitude of the force P, (b) the tension in the cord AD. Neglect
the masses of the pulleys and axle friction.
SOLUTION
PROBLEM 12.28 (Continued)
AD BC
AD
PROBLEM 12.29
A 40-lb sliding panel is supported by rollers at B and C. A 25-lb counterweight A is attached to a cable as
shown and, in cases a and c, is initially in contact with a vertical edge of the panel. Neglecting friction,
determine in each case shown the acceleration of the panel and the tension in the cord immediately after the
system is released from rest.
SOLUTION
PROBLEM 12.29 (Continued)
2
12.38 ft/s=a
;
15.38 lbT=
PROBLEM 12.30
An athlete pulls handle A to the left with a constant
force of P = 100 N. Knowing that after the handle
A has been pulled 30 cm its velocity is 3 m/s,
determine the mass of the weight stack B.
SOLUTION
B
PROBLEM 12.31
A 10-lb block B rests as shown on a 20-lb bracket A. The
coefficients of friction are
0.30
s
µ
=
and
0.25
k
µ
=
between
block B and bracket A, and there is no friction in the pulley or
between the bracket and the horizontal surface. (a) Determine
the maximum weight of block C if block B is not to slide on
bracket A. (b) If the weight of block C is 10% larger than the
answer found in a determine the accelerations of A, B and C.
SOLUTION
PROBLEM 12.31 (Continued)
AB s AB s B
PROBLEM 12.31 (Continued)
C
PROBLEM 12.32
Knowing that µ = 0.30, determine the acceleration of each block when
mA = mB = mC.
Given:
0.30
ABc
mmmm
µ
=
= = =
Problem 12.32 (Continued)
6
T
C
C
PROBLEM 12.33
Knowing that µ = 0.30, determine the acceleration of each block
when mA = 5 kg, mB = 30 kg, and mC = 15 kg.
SOLUTION
Given:
2
0.30, 9.81 m/s
5 kg, 30 kg, 15 kg
AB C
g
mm m
µ
= =
= = =
Problem 12.33 (Continued)
T
C
C
PROBLEM 12.34
A 25-kg block A rests on an inclined surface, and a 15-kg counterweight
B is attached to a cable as shown. Neglecting friction, determine the
acceleration of A and the tension in the cable immediately after the
system is released from rest.
SOLUTION
Let the positive direction of
x and y be those shown in the sketch, and let
the origin lie at the cable anchor.
PROBLEM 12.35
Block B of mass 10-kg rests as shown on the upper surface of a 22-kg
wedge A. Knowing that the system is released from rest and neglecting
friction, determine (a) the acceleration of B, (b) the velocity of B relative to
A at
0.5 s.t=
2
2
(9.81sin 20 6.4061cos50 ) m/s
7.4730 m/s
= °+ °
=
PROBLEM 12.35 (Continued)
/
BA
