* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Lecture 13 - McMaster Physics and Astronomy
Survey
Document related concepts
Noether's theorem wikipedia , lookup
Theory of everything wikipedia , lookup
Renormalization wikipedia , lookup
Monte Carlo methods for electron transport wikipedia , lookup
Standard Model wikipedia , lookup
Atomic nucleus wikipedia , lookup
Relativistic quantum mechanics wikipedia , lookup
Nuclear structure wikipedia , lookup
ATLAS experiment wikipedia , lookup
Large Hadron Collider wikipedia , lookup
Renormalization group wikipedia , lookup
Elementary particle wikipedia , lookup
Theoretical and experimental justification for the Schrödinger equation wikipedia , lookup
Peter Kalmus wikipedia , lookup
ALICE experiment wikipedia , lookup
Electron scattering wikipedia , lookup
Transcript
Collisions • Conservation of Momentum • Elastic and inelastic collisions Physics 1D03 - Lecture 26 Collisions A collision is a brief interaction between two (or more) objects. We use the word “collision” when the interaction time Δt is short relative to the rest of the motion. During a collision, the objects exert equal and opposite forces on each other. We assume these “internal” forces are much larger than any external forces on the system. We can ignore external forces if we compare velocities just before and just after the collision, and if the interaction force is much larger than any external force. v1,i m1 v2,i m2 F1 F2 = -F1 v1,f v2,f Physics 1D03 - Lecture 26 Elastic and Inelastic Collisions Momentum is conserved in collisions. Kinetic energy is sometimes conserved; it depends on the nature of the interaction force. A collision is called elastic if the total kinetic energy is the same before and after the collision. If the interaction force is conservative, a collision between particles will be elastic (eg: billiard balls). If kinetic energy is lost (converted to other forms of energy), the collision is called inelastic (eg: tennis ball and a wall). A completely inelastic collision is one in which the two colliding objects stick together after the collision (eg: alien slime and a spaceship). Kinetic energy is lost in this collision. Physics 1D03 - Lecture 26 If there are no external forces, then the total momentum is conserved: v1,i m1 v2,i m2 p1,i + p2,i = p1,f + p2,f v1,f v2,f This is a vector equation. It applies to each component of p separately. Physics 1D03 - Lecture 26 Elastic Collisions In one dimension (all motion along the x-axis): 1) Momentum is conserved: m1v1i m2 v2i m1 v1f m2v2f In one dimension, the velocities are represented by positive or negative numbers to indicate direction. 2) Kinetic Energy is conserved: 1 2 m1v12i 12 m2v22i 12 m1v12f 12 m2v22f We can solve for two variables if the other four are known. Physics 1D03 - Lecture 26 One useful result: for elastic collisions, the magnitude of the relative velocity is the same before and after the collision: |v1,i – v2,i | = |v1,f – v2,f | (This is true for elastic collisions in 2 and 3 dimensions as well). An important case is a particle directed at a stationary target (v2,i = 0): • Equal masses: If m1 = m2, then v1,f will be zero (1-D). • If m1 < m2, then the incident particle recoils in the opposite direction. • If m1 > m2, then both particles will move “forward” after the collision. before after Physics 1D03 - Lecture 26 Elastic collisions, stationary target (v2,i = 0): Two limiting cases: 1) If m1 << m2 , the incident particle rebounds with nearly its original speed. v1 -v1 2) If m1 >> m2 , the target particle moves away with (nearly) twice the original speed of the incident particle. v1 v1 2v1 Physics 1D03 - Lecture 26 Concept Quiz A tennis ball is placed on top of a basketball and both are dropped. The basketball hits the ground at speed v0. What is the maximum speed at which the tennis ball can bounce upward from the basketball? (For “maximum” speed, assume the basketball is much more massive than the tennis ball, and both are elastic). a) v0 b) 2v0 c) 3v0 ? v0 v0 Physics 1D03 - Lecture 26 Example A mad 60.0 kg physicist standing on a frozen lake throws a 0.5 kg stone to the east with a speed of 24.0 m/s. Find the recoil velocity of the mad physicist. Physics 1D03 - Lecture 26 Example – inelastic collision: A neutron, with mass m = 1 amu (atomic mass unit), travelling at speed v0, strikes a stationary deuterium nucleus (mass 2 amu), and sticks to it, forming a nucleus of tritium. What is the final speed of the tritium nucleus? Physics 1D03 - Lecture 26 An elastic collision: Two carts moving toward each other collide and bounce back. If cart 1 bounces back with v=2m/s, what is the final speed of cart 2 ? 6 m/s 2 kg 5 m/s 4 kg Physics 1D03 - Lecture 26 Example A bullet of mass m is shot into a block of mass M that is at rest on the edge of a table. If the bullet embeds in the block, determine the velocity of the bullet if they land a distance of x from the base of the table, which has a height of h. Physics 1D03 - Lecture 26