Mechanical Engineering Principles

142 MECHANICAL ENGINEERING PRINCIPLES

(c) Resistive force of ground=mass×accelera-
tion. The acceleration is determined using
v^2 =u^2 + 2 aswherev=final velocity=0,
u = initial velocity = 3 .49 m/s and s =
distance driven in ground=200 mm= 0 .2m.

Hence, 02 =( 3. 49 )^2 + 2 (a)( 0. 2 ),

from which,

acceleration, a=

−( 3. 49 )^2

2 ( 0. 2 )

=− 30 .45 m/s^2

(the minus sign indicates retardation)

Thus,resistive force of ground

=mass×acceleration

=1100 kg× 30 .45 m/s^2

= 33 .5kN

Now try the following exercise

Exercise 60 Further problems on impulse

and impulsive forces

(Where necessary, takegas 9.81 m/s^2 )

1. The sliding member of a machine tool
   has a mass of 200 kg. Determine the
   change in momentum when the slid-
   ing speed is increased from 10 mm/s to
   50 mm/s. [8 kg m/s]


2. A force of 48 N acts on a body of mass
   8 kg for 0.25 s. Determine the change in
   velocity. [1.5 m/s]


3. The speed of a car of mass 800 kg
   is increased from 54 km/h to 63 km/h
   in 2 s. Determine the average force in
   the direction of motion necessary to pro-
   duce the change in speed. [1000 N]


4. A 10 kg mass is dropped vertically on
   to a fixed horizontal plane and has an
   impact velocity of 15 m/s. The mass
   rebounds with a velocity of 5 m/s. If
   the contact time of mass and plane is
   0.025 s, calculate (a) the impulse, and
   (b) the average value of the impulsive
   force on the plane.

[(a) 200 kg m/s (b) 8 kN]

5. The hammer of a pile driver of mass
   1.2 t falls 1.4 m on to a pile. The blow
   takes place in 20 ms and the hammer
   does not rebound. Determine the average
   applied force exerted on the pile by the
   hammer. [314.5 kN]


6. A tennis ball of mass 60 g is struck
   from rest with a racket. The contact
   time of ball on racket is 10 ms and the
   ball leaves the racket with a velocity of
   25 m/s. Calculate (a) the impulse, and
   (b) the average force exerted by a racket
   on the ball.

[(a) 1.5 kg m/s (b) 150 N]

7. In a press-tool operation, the tool is in
   contact with the workpiece for 40 ms. If
   the average force exerted on the work-
   piece is 90 kN, determine the change in
   momentum. [3600 kg m/s]


8. A gun of mass 1.2 t fires a shell of mass
   12 kg with a velocity of 400 m/s.
   Determine (a) the initial velocity of
   recoil, and (b) the uniform force nec-
   essary to stop the recoil of the gun in
   150 mm.

[(a) 4 m/s (b) 64 kN]

9. In making a steel stamping, a mass of
   100 kg falls on to the steel through a
   distance of 1.5 m and is brought to rest
   after moving through a further distance
   of 15 mm. Determine the magnitude
   of the resisting force, assuming a
   uniform resistive force is exerted by the
   steel.
   [98.1 kN]


10. A vertical pile of mass 150 kg is driven
    120 mm into the ground by the blow
    of a 1.1 t hammer which falls through
    800 mm. Assuming the hammer and
    pile remain in contact, determine (a) the
    velocity of the hammer just before
    impact, (b) the velocity immediately
    after impact, and (c) the resistive force
    of the ground, assuming it to be
    uniform.

[(a) 3.96 m/s (b) 3.48 m/s

(c) 63.08 kN]