Chapter 7 Impulse and Momentum. So far we considered only constant force/s BUT There are many situations when the force on an object is not constant

Transcription

1 Chapter 7 Ipulse and Moentu So far we considered only constant force/s BUT There are any situations when the force on an object is not constant

2 Force varies with tie

3 7. The Ipulse-Moentu Theore DEFINITION OF IMPULSE The ipulse of a force is the product of the average force and the tie interval during which the force acts. J = F t Ipulse is a vector quantity and has the sae direction as the average force. Units? Newton seconds (N s) kg s

4 7. The Ipulse-Moentu Theore J = F t

5 7. The Ipulse-Moentu Theore DEFINITION OF LINEAR MOMENTUM The linear oentu of an object is the product of the object s ass ties its velocity p = v Moentu is a vector quantity and has the sae direction as the velocity Units? kilogra eter/second (kg /s) N s

6 7. The Ipulse-Moentu Theore a v f v t = o F = a F v =( f v o t ) ( ) F t = v v f o J = pp ff pp oo

7 7. The Ipulse-Moentu Theore IMPULSE-MOMENTUM THEOREM When a net force acts on an object, the ipulse of this force is equal to the change in the linear oentu of the object ( ) F t J = pp Original for of Newton s Law of otion v f v o final oentu ( ) F t = v v f o initial oentu

8 7. The Ipulse-Moentu Theore Exaple: A Rain Stor Rain coes down with a velocity of -5 /s and hits the roof of a car. The ass of rain per second that strikes the roof of the car is kg/s. Assuing that rain coes to rest upon striking the car, find the average force exerted by the rain on the roof. ( ) F t = v f vo F = F= t v o ( kg s)( 5 s) N

9 7. The Principle of Conservation of Linear Moentu WORK-ENERGY THEOREM (Ch. 6) CONSERVATION OF ENERGY IMPULSE-MOMENTUM THEOREM??? Apply the ipulse-oentu theore to the idair collision between two objects Internal forces Forces that objects within the syste exert on each other. External forces Forces exerted on objects by agents external to the syste.

10 7. The Principle of Conservation of Linear Moentu Ipulse-Moentu Theore ( F) t = v f vo OBJECT ( ) W + F t = v f v o OBJECT ( ) W + F t = v f vo

11 7. The Principle of Conservation of Linear Moentu ( ) W + F t = v f v o + ( ) W + F t = v f vo ( ) W + W + F + F t = ( v + v ) ( v + v ) f f o o But F = F The internal forces cancel out. ( W + ) t = W pp f ( su of external forces) t = pp f pp oo pp f pp oo pp o

12 7. The Principle of Conservation of Linear Moentu ( su of average external forces) t = pp f pp oo If the su of the external forces is zero, then 0 = pp f pp oo pp f = pp oo PRINCIPLE OF CONSERVATION OF LINEAR MENTUM If the su of external forces is zero, the total linear oentu of the syste is constant (conserved) The total linear oentu of an isolated syste is constant (conserved). An isolated syste is one for which the su of the external forces acting on the syste is zero.

13 7. The Principle of Conservation of Linear Moentu Applying the Principle of Conservation of Linear Moentu. Decide which objects are included in the syste.. Relative to the syste, identify the internal and external forces. 3. Verify that the syste is isolated. 4. Set the final oentu of the syste equal to its initial oentu. Reeber Moentu is a vector Decide positive and negative directions in the start.

14 Question: A ball of ass hits a wall horizontally with speed v and bounces back with sae speed. Which of the following is right to say about linear oentu and KE of the ball? a) Both oentu and KE of the ball are conserved. b) Both oentu and KE of the ball are not conserved. c) Only oentu of the ball is conserved. d) Only KE of the ball is conserved. Isolated syste? Exaple: Starting fro rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woan and other is 88-kg an. The woan oves away with a speed of +.5 /s. Find the recoil velocity of the an.

15 7. The Principle of Conservation of Linear Moentu Exaple: Starting fro rest, two skaters push off against each other on ice where friction is negligible. One is a 54-kg woan and other is 88-kg an. The woan oves away with a speed of +.5 /s. Find the recoil velocity of the an. Syste here is both skaters Before the push pp 0 = vv ooo + vv ooo pp 0 = 0 After the push pp ff = vv fff + vv fff Conservation of Linear oentu pp f = pp oo vv fff= - vv fff + vv fff = 0 vv fff -.53 /s

16 7.3 Collisions in One Diension Collision: The total linear oentu is conserved when two objects collide, provided they constitute an isolated syste. Two Types of Collison Elastic collision -- One in which the total kinetic energy of the syste after the collision is equal to the total kinetic energy before the collision. Inelastic collision -- One in which the total kinetic energy of the syste after the collision is not equal to the total kinetic energy before the collision; if the objects stick together after colliding, the collision is said to be copletely inelastic.

17 7.3 Collisions in One Diension Exaple: A Ballistic Pendulu The ass of the block of wood is.50-kg and the ass of the bullet is kg. The block swings to a axiu height of above the initial position. Find the initial speed of the bullet. Syste? Bullet and block Linear Moentu will be conserved Type of collision? Copletely Inelastic KE will not be conserved Mechanical Energy will be conserved Speed of bullet = 896 /s

18 7.4 Collisions in Two Diensions Before collision x- coponent of p 0 p0 x = v ox + vo x v = v ox o v o x = v 0 Sin(50 p + o 0 x = v osin( 50 ) vo o ) A Collision in Two Diensions 0.44 kg /s vv fff? y- coponent of p 0 = v v p0 y oy + o y v = v oy v o y = 0 o Cos(50 o ) p = v 0 y o Cos(50 o ) kg /s

19 After collision x- coponent p fx = v f x + v f x v f x = v f Cosθ p = v Cosθ + v fx v = v f x f y- coponent f Cos(35 f p fy = v f y + v f y v f y = v f v = v f y Sinθ f o ) Sin(35 o ) Cos(35 o ) p fy = v Sinθ v f f Sin(35 o )

20 7.4 Collisions in Two Diensions Conservation of linear oentu pp ffff = pp oooo And pp ffff = pp oooo v v f x + v f x = ox + ox v f y + v f y = v oy + vo y v Cos(35 o v f Cosθ + v f = ) 0.44 And v f Cosθ = 0.63 / s o v Sinθ v Sin(35 ) = f f v f Sinθ = 0.6 / s vv fff = 0.64 /ss θ = And

21 7.5 Center of Mass Center of Mass The center of ass is a point that represents the average location for the total ass of a syste. = x x c + + x

22 7.5 Center of Mass x x x c + + = v v v c + + = Velocity of center of ass p p v c + + =

23 Question: A ball hits the floor with a speed v. It bounces back with exact sae speed. Which of the following is true? a) The velocity of the ball is conserved. b) Both linear oentu and kinetic energy of the ball are conserved. c) Only linear oentu of the ball is conserved. d) Only kinetic energy of the ball is conserved. Question: A car and a bicycle oving side by side with sae velocity. Which of the followings is true a) Both have sae oentu. b) Both require equal ipulse to bring the to halt. c) Car needs larger ipulse to bring it to halt. d) None of the above.

24 Question: A collision is called elastic if a) The final velocity is zero. b) The initial velocity is zero. c) Both linear oentu and kinetic energy are not conserved. d) Both linear oentu and kinetic energy are conserved. Proble: A 4000 kg truck traveling due North with a speed of 40 /s collides head-on with a 00 kg car standing on the road. Two vehicles stick together after the collision. What is their velocity just after the collision (agnitude and direction)?

25 Proble 34 (Textbook) The drawing shows a collision between two pucks on an air-hockey table. Puck A has a ass of 0.05 kg and is oving along the x axis with a velocity of +5.5 /s. It akes a collision with puck B, which has a ass of kg and initially at rest. The collision is not headon. After the collision, the two pucks fly apart with the angles shown in the drawing. Find the final speed of a) puck A and b) puck B A a) vv ffa = 3.4 /ss A B 65 o 37 o b) vv ffb =.6 /ss B Before collision After collision

26 Ipulse Suary of Ch. 7 J = F t Linear Moentu p = v kg OR N ss s Ipulse-Moentu Theore J = pp Principle of Conservation of Linear Moentu The total linear oentu of an isolated syste is constant (conserved). pp f = pp oo -D v + v = v + f f o o -D v f y + v f y = v oy + vo y v f x + v f x = v ox + vo x v x x = c + + x v v = c + + v = p + + p

27 For Recitation Practice Chapter 7 FOC:,, 7, 0, 3 & 5. Probles: 4,, 9, 5, 34 & 59. Reading Assignent for next class Chapter 8: 8. to 8.3