PROBLEM 14.104
In a rocket, the kinetic energy imparted to the consumed and ejected fuel is wasted as far as propelling the
rocket is concerned. The useful power is equal to the product of the force available to propel the rocket and
the speed of the rocket. If v is the speed of the rocket and u is the relative speed of the expelled fuel, show that
the mechanical efficiency of the rocket is 22
2/( ).uv u v
Explain why 1
when .uv
PROBLEM 14.105
Three identical cars are being unloaded from an
automobile carrier. Cars B and C have just been
unloaded and are at rest with their brakes off when car A
leaves the unloading ramp with a velocity of 5.76 ft/s
and hits car B, which hits car C. Car A then again hits
car B. Knowing that the velocity of car B is 5.04 ft/s
after the first collision, 0.630 ft/s after the second
collision, and 0.709 ft/s after the third collision,
determine (a) the final velocities of cars A and C, (b) the
coefficient of restitution for each of the collisions.
PROBLEM 14.106
A 30-g bullet is fired with a velocity of 480 m/s into block A,
which has a mass of 5 kg. The coefficient of kinetic friction
between block A and cart BC is 0.50. Knowing that the cart
has a mass of 4 kg and can roll freely, determine (a) the final
velocity of the cart and block, (b) the final position of the
block on the cart.
PROBLEM 14.107
An 80-Mg railroad engine A coasting at 6.5 km/h strikes a 20-Mg flatcar C carrying a 30-Mg load B that can
slide along the floor of the car
(0.25).
k
Knowing that the car was at rest with its brakes released and that
it automatically coupled with the engine upon impact, determine the velocity of the car (a) immediately after
impact, (b) after the load has slid to a stop relative to the car.
PROBLEM 14.107 (Continued)
PROBLEM 14.108
In a game of pool, ball A is moving with a velocity
v
0
when it strikes
balls B and C which are at rest and aligned as shown. Knowing that
after the collision the three balls move in the directions indicated and
that
0
12 ft/sv
and
6.29 ft/s,
C
v
determine the magnitude of the
velocity of (a) ball A, (b) ball B.
PROBLEM 14.109
Mass C, which has a mass of 4 kg, is suspended from a cord attached to cart
A, which has a mass of 5 kg and can roll freely on a frictionless horizontal
track. A 60-g bullet is fired with a speed v0 500 m/s and gets lodged in
block C. Determine (a) the velocity of C as it reaches its maximum elevation,
(b) the maximum vertical distance h through which C will rise.
PROBLEM 14.109 (Continued)
PROBLEM 14.109 (Continued)
PROBLEM 14.110
A 15-lb block B is at rest and a spring of constant
k
72
lb/in. is held compressed 3 in. by a cord. After
5-lb block A is placed against the end of the spring, the
cord is cut causing A and B to move. Neglecting
friction, determine the velocities of blocks A and B
immediately after A leaves B.