To introduce the concepts of position, displacement, velocity, and acceleration. To study, Slides of Dynamics

Download To introduce the concepts of position, displacement, velocity, and acceleration. To study and more Slides Dynamics in PDF only on Docsity!

KINETICS OF A PARTICLE: IMPLUSE &

MOMENTUM

^  CHAPTER OBJECTIVESCHAPTER OBJECTIVES

 (^) To develop the principle of linear impulse and momentum for a particle

and apply it to solve problems that involve force, velocity, and time.

 (^) To study the conservation of linear momentum for particles.

 (^) To analyze the mechanics of impact.

 (^) To introduce the concept of angular impulse and momentum.

 (^) To solve problems involving steady fluid streams and propulsion with

variable mass.

KINETICS OF A PARTICLE: IMPLUSE &

MOMENTUM

the principle of linear impulse and momentum^ the principle of linear impulse and momentum

PRINCIPLE OF LINEAR IMPLUSE AND

MOMENTUM

PRINCIPLE OF LINEAR IMPLUSE AND

MOMENTUM

^  EXAMPLE 15.1 – PAGE 225EXAMPLE 15.1 – PAGE 225

The 100-kg stone shown in Fig. 15-4a is

originally at rest on the smooth horizontal

surface. If a towing force of 200N, acting

at an angle of 45^0 , is applied to the stone

for 10s, determine the final velocity and

the normal force which the surface exerts

on the stone during this time interval.

PRINCIPLE OF LINEAR IMPLUSE AND

MOMENTUM

^  EXAMPLE 15.2 – PAGE 226EXAMPLE 15.2 – PAGE 226

The 50-lb crate shown in Fig. 15-5a is acted upon by a force having a variable

magnitude P =(20 t )lb, where t is in seconds. Determine the crate's velocity 2s

after P has been applied. The initial velocity is v 1 =3ft/s down the plane, and

the coefficient of kinetic friction between the crate and the plane is  k =0.

PRINCIPLE OF LINEAR IMPLUSE AND

MOMENTUM

^  EXAMPLE 15.3 – PAGE 227EXAMPLE 15.3 – PAGE 227

Blocks A and B shown in Fig. 15-6a have

a mass of 3kg and 5kg, respectively. If the

system is released from rest, determine

the velocity of block B in 6s. Neglect the

mass of the pulleys and cord.

PRINCIPLE FOR A SYSTEM OF

PARTICLES

The mass center G of the system

The mass center G of the system

PRINCIPLE FOR A SYSTEM OF

• •  PROBLEMS F15.1  F15. PARTICLES
    • 15.2 15.5 15.
    • 15.25 15.26 15.
  •  PROBLEMS F15.1  F15.
    • 15.2 15.5 15.
    • 15.25 15.26 15.

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.4 – PAGE 238EXAMPLE 15.4 – PAGE 238

The 15-Mg boxcar A is coasting at

1.5m/s on the horizontal track when it

encounters a 12-Mg tank car B

coasting at 0.75m/s toward it as shown

in Fig. 15-8a. If the cars collide and

couple together, determine:

(a) the speed of both cars just after the

coupling

(b)the average force between them if

the coupling takes place in 0.8s

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.5 – PAGE 239EXAMPLE 15.5 – PAGE 239

The 1200-lb cannon shown in the Fig.

fires an 8-lb projectile with a muzzle

velocity of 1500 ft/s relative to the

ground. If firing takes place in 0.03s,

determine:

(a) the recoil velocity of the cannon

just after firing.

(b)the average impulsive force acting

on the projectile. The cannon

support is fixed to the ground, and

the horizontal recoil of the cannon

is absorbed by two springs.

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.6 – PAGE 240EXAMPLE 15.6 – PAGE 240

The bumper cars A and B in Fig. 15-10a

each have a mass of 150kg and are

coasting with the velocities shown before

they freely collide head on. If no energy

is lost during the collision, determine

their velocities after collision.

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.7 – PAGE 241EXAMPLE 15.7 – PAGE 241

An 800-kg rigid pile shown in Fig. I5-

11a is driven into the ground using a

300-kg hammer. The hammer falls from

rest at a height y 0 =0.5m and strikes the

top of the pile. Determine the impulse

which the pile exerts on the hammer if

the pile is surrounded entirely by loose

sand so that after striking, the hammer

does not rebound off the pile.

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.7 – PAGE 241EXAMPLE 15.7 – PAGE 241

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE 15.8 – PAGE 242EXAMPLE 15.8 – PAGE 242

The 1.5-Mg car in Fig. 15-12a moves

on the 10-Mg barge to the left with a

constant speed of 4m/s, measured

relative to the barge. Neglecting water

resistance, determine the velocity of

the barge and the displacement of the

barge when the car reaches point B.

Initially, the car and the barge are at

rest relative to the water.

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

^  EXAMPLE *EXAMPLE *

CONSERVATION Of A LINEAR MOMENTUM For a

SYSTEM

 FUNDAMENTAL PROBLEMS F15.7  F15.

 15.33 15.39 15.41 15.50 15.

 FUNDAMENTAL PROBLEMS F15.7  F15.

 15.33 15.39 15.41 15.50 15.

15.4 IMPACT

15.4 IMPACT – CENTRAL IMPACT

15.4 IMPACT – CENTRAL IMPACT

15.4 IMPACT – CENTRAL IMPACT

15.4 IMPACT – CENTRAL IMPACT

15.4 IMPACT – CENTRAL IMPACT

15.4 IMPACT – OBLIQUE IMPACT

IMPAC

T

^  (^) EXAMPLE 15.9EXAMPLE 15.9 - Page 252- Page 252

The bag A, having a weight of 6lb, is released

from rest at the position =0°, as shown in the

Fig. After falling to =90°, it strikes an 18-lb

box B. If the coefficient of restitution between

the bag and box is e =0.5, determine the

velocities of the bag and box just after impact.

What is the loss of energy during collision?