Collisions. Lecture 18. Chapter 11. Physics I. Department of Physics and Applied Physics

Transcription

1 Lecture 18 Chater 11 Physics I Collisions Course website: htt://faculty.uml.edu/ndriy_danylov/teaching/physicsi Deartment of Physics and lied Physics

2 IN THIS CHPTER, you will discuss collisions of two objects Today we are going to discuss: Chater 11: 1D Collisions (Elastic/Inelastic): Section 11.3 D Collisions (Elastic/Inelastic): Section 11.3 Center of Mass: Section 1. Deartment of Physics and lied Physics

3 Review 1.. Linear momentum: Newton s nd law: mv F m a F d dt (This form is more general) 3. We alied N. nd law to an interaction of objects: If F ext F 0 dp dt Internal forces cancel each other dp, then 0 dt, thus P const P in P fin F ext P dp dt 1 Conservation of linear momentum m v m v m v m v Conservation of momentum Deartment of Physics and lied Physics

4 Different tyes of collisions Linear momentum is conserved in both of these two-body collisions (since there is no net external force) Is mechanical energy conserved in these collisions? Metal balls get deformed and restored Mech. energy is conserved Elastic collision Cars get deformed and not restored. Some Mech. Energy is sent on deformation. Mech. energy is NOT conserved Inelastic collision Deartment of Physics and lied Physics

5 Examle allistic Pendulum device used to measure the seed of a bullet. This an examle of inelastic collision. Mechanical Energy here is not conserved. (Lots of energy is used to damage the wooden block.) ut the linear momentum is still conserved. For ullet mass 10 g lock mass is 3 kg lock swings u to a height of 5 cm the seed of a bullet Deartment of Physics and lied Physics v o 98 m s

6 In the revious examle we discussed the inelastic collision (1D). Linear momentum is conserved Mech. Energy is not conserved = 1-D Elastic Head-On Collisions Now, we are going to discuss an elastic head-on collision (1D). Linear momentum is conserved Mech. Energy is conserved = Deartment of Physics and lied Physics

7 initial Conservation of momentum m v m v m v m m v m v m v m v mv m (v v ) m ( v v ) Elastic Head-on Collision (1D) mv v final Relative velocities switch signs in the collision Conservation of mech. energy (ELSTIC) ' ' ' K K U U K K U U 1 m v 1 m v 1 m v 1 m v m v m v m v m v m (v v ) m ( v v ) m (v v )(v v ) m ( v v )( v v ) v v v v v v v v ) m v mv ( 0. ' Deartment of Physics and lied Physics So, instead of the 1 st set of crazy (quadratic) equations, we can use the nd one which is easier (both are linear). It is only true for an elastic head-on collision

8 Examle 1D head-on collision ball of mass 0.0 kg that is moving with a seed of 7.5 m/s collides head-on and elastically with another ball initially at rest. Immediately after the collision, the incoming ball bounces backward with a seed of 3.8 m/s. Calculate: a) the velocity of the target ball after the collision; b) the mass of the target ball. eq-ns Deartment of Physics and lied Physics

9 Collisions in D You know how to figure out the results of a collision between objects in 1D: -use conservation of momentum- and, -if collision is elastic, conservation of mech. energy. You can continue to use the same rules in D collisions as follows: If If ext F y ext F x 0, then momentum in x - direction is conserved initial x initial y final x 0, then momentum in y - direction is conserved final y Mech. Energy is conserved in elastic collisions (not in each dimension) mv mv ( ) initial ( ) final Deartment of Physics and lied Physics

10 Examle Collisions in D: Momentum Conservation Since net external forces in x and y directions are zero, linear momentum in x and y directions are conserved X mv before x m v after x m v ' cos mv' cos rojectile (m ) moves along the x-axis and hits a target (m ) at rest. fter the collision, the two objects go off at different angles. y m v Y before y m v' after y sin ' 0 m v' sin ' Two equations, can be solved for two unknowns ut, sometimes, these eq-ns aren t enough m v v m 0 x If collision is elastic, we can get the third equation (conservation of mechanical energy) 1 m v 1 m v' 1 m v' Three equations, can be solved for three unknowns Careful!!! in -D collisions v v m ( v v ) It cannot be used v Deartment of Physics and lied Physics

11 all moving at 4 m/s strikes ball (of equal mass) at rest. fter the collision, ball travels forward at an angle of +45º, and ball travels forward at -45º. What are the final seeds of the two balls? conservation of y-momentum: 0 mv' sin 45 mv' sin(45) 0 v' sin 45 v' sin 45 v' v' m v y m v 45 x conservation of x-momentum: m( 4 m ) mv' cos 45 mv' cos(45) s v m 0 45 m 4 ( 1 )v' ( 1 )v' v 4 v' v' v' 4 v' m/ s v' v' Deartment of Physics and lied Physics

12 Deartment of Physics and lied Physics Thank you See you on Monday