Download Momentum-Classical Physics-Handouts and more Lecture notes Classical Physics in PDF only on Docsity! PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 22 Summary of Lecture 9 – MOMENTUM 1. Momentum is the "quantity of motion" possessed by a body. More precisely, it is defined as: The dimensions of momentum are . Mass of the body × Velocity of the body -1 and the units of momentum are kg-m/s. 2. Momentum is a vector quantity and has both magnitude and direction, v. We can easily see that Newton's Second Law can be reexpressed in terms MLT p m= of momentum. When v I wrote it down originally, it was in the form a . But since a, this can also be written as (new form). In words, the rate of change of momentum of a bod dm dt d dt = = = F p F y equals the total force acting upon it. Of course, the old and new are exactly the same, ( ) . 3. When there are many particles, then th d d m dm m dt dt dt = = = = p v v a F 1 2 1 2 1 2 e total momentum is, Thi N N N d d d d dt dt dt dt = + + ⋅ ⋅ ⋅ = + + ⋅ ⋅ ⋅ = + + ⋅ ⋅ ⋅ = P P p p p p p pP F F F F s shows that when there are several particles, the rate at which the total momentum changes is equal to the total force. It makes sense! 4. A very important conclusion of the above is that if the sum of the total external forces vanishes, then the total momentum is conserved, 0 = 0. This is quite independent of what sort of forces act between the bodies - electric, gravitati ext dF dt = ⇒∑ P onal, etc. - or how complicated these are. We shall see why this is so important from the following examples. 5. Two balls, which can only move along a straight line, collide with each other. The 1 1 2 2 1 1 2 2 initial momentum is and the final momentum is v v . Obviously one ball exerts a force on the other when they collide, so its momentum changes. But, from the fact that th i fP m u m u P m m= + = + 1 1 2 2 1 1 2 2ere is no external force acting on the balls, , or v v . 6. A bomb at rest explodes into two fragments. Before the explosion the total momentum is i fP P m u m u m m= + = + docsity.com PHYSICS –PHY101 VU © Copyright Virtual University of Pakistan 23 zero. So obviously it is zero after the explosion as well, . During the time that the explosion happens, the forces acting upon the pieces are very complicated and changing rapidly with f =P 0 1 1 2 2 1 1 2 2 time. But when all is said and done, there are two pieces flying away with a total zero final momentum v v . Hence v v . In other words, the fragments fly apart with equal momentum f m m m m= + = −P but in opposite directions. The centre-of-mass stays at rest. So, knowing the velocity of one fragment permits knowing the velocity of the other fragment. 0 7. If air resistance can be ignored, then we can do some interesting calculations with what we have learned. So, suppose a shell is fired from a cannon with a speed 10 m/s at an angle 60 with the horizontal. At the highest point in its path it explodes into two pieces of equal masses. One of the pieces retraces its path to the cannon. Let us find the velocity of the other piec 1 1 2 2 2 2 2 e immediately after the explosion. Solution: After the explosion: 5 (why?). But 10cos60 2 5 5 . Now use: v v 15 / . 2 2 8. When yo x x x x x x x x MP P P P M M MP M P m s = − + = = × ⇒ = + = ⇒ = u hit your thumb with a hammer it hurts, doesn't it? Why? Because a large amount of momentum has been destroyed in a short amount of time. If you wrap your thumb with foam, it will hurt less. To understand this better, remember that force is the rate of change of momentum: . Now define the as: dpF dp Fdt I dt = ⇒ = impulse force × time over which the 2 2 1 1 If the force changes with time between the limits , then one should define as, . Since , therefore . In words, the change of momentum equal f i pt t f i pt t I I Fdt Fdt dp I p p= = = −∫ ∫ ∫ force acts. s the impulse, which is equal to the area under the curve of force versus time. Even if you wrap your thumb in foam, the impulse is the same. But the force is definitely not! docsity.com
