PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 9 Last Lecture Momentum r r p mv r pr F t Newton s 2nd Conserved for isolated objects Impulse F t p Useful for short times Collisions p always conserved Elastic E conserved too Inelastic E not conserved Example 6 7 A proton mp 1 67x10 27 kg elastically collides with a target proton which then moves straight forward If the initial velocity of the projectile proton is 3 0x106 m s and the target proton bounces forward what are a the final velocity of the projectile proton b the final velocity of the target proton 0 0 3 0x106 m s Elastic collision in 1 dimension 1 Conservation of Energy 2 2 2 2 1 1 1 1 m v m v m v m v 1 1i 2 2i 2 2f 2 2 2 1 1f 2 1 2 Conservation of Momentum m1v1i m 2v 2i m1v1 f m 2v 2 f 2 Rearrange both equations and divide m1 v1i2 v12f m2 v 22 f v 2i2 1 m1 v1i v1 f v1i v1 f m 2 v 2 f v 2i v 2 f v 2i m1 v1i v1 f m2 v 2 f v 2i v1i v1 f v 2 f v 2i v1i v 2i v1 f v 2 f 2 Elastic collision in 1 dimension Final equations for head on elastic collision m1v1i m 2v 2i m1v1 f m2v 2 f v1i v 2i v1 f v 2 f Relative velocity changes sign Equivalent to Conservation of Energy p d Example 6 8 An proton mp 1 67x10 27 kg elastically collides with a target deuteron mD 2mp which then moves straight forward If the initial velocity of the projectile proton is 3 0x106 m s and the target deuteron bounces forward what are a the final velocity of the projectile proton b the final velocity of the target 6 1 0x10 m s deuteron 2 0x106 m s ead on collisions with heavier objects always lead eflections Example 6 9a The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at a rest Just after the collision v2 v0 The collision is perfectly elastic A B C Example 6 9b The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision v1 0 A B C Example 6 9c The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision P2 M1v0 A B C Example 6 9d The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic At maximum compression the energy stored in the spring is 1 2 M1v02 A B C Example 6 9e The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision v2 v0 A B C Example 6 9f The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision v1 0 A B C Example 6 9g The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision P2 M1v0 A B C Example 6 9h The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic At maximum compression the energy stored in the spring is 1 2 M1v02 A B C Example 6 9i The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision v2 v0 A B C Example 6 9j The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision v1 0 A B C Example 6 9k The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic Just after the collision P2 M1v0 A B C Example 6 9l The mass M1 enters from the left with velocity v0 and strikes the mass M2 M1 which is initially at rest The collision is perfectly elastic At maximum compression the energy stored in the spring is 1 2 M1v02 A B C Example 6 10 Ballistic Pendulum used to measure speed of bullet 0 5 kg block of wood swings up by height h 65 cm after stopping 8 0 g bullet What was bullet s velocity 227 m s Example 6 11 A 5 g bullet traveling at 500 m s embeds in a 1 495 kg block of wood resting on the edge of a 0 9 m high table How far does the block land from the edge of the table 71 4 cm Example 6 12 Tarzan M 80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m 50 kg To what angle do Tarzan and Jane swing 35 8 degrees indepedent of L or g Example 6 12a Tarzan M 80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m 50 kg To what angle do Tarzan and Jane swing To calculate Tarzan s speed just before he picks up Jane you should apply A Conservation of Energy B Conservation of Momentum Example 6 12b Tarzan M 80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m 50 kg To what angle do Tarzan and Jane swing To calculate Tarzan Jane s speed just after their collision given the previous answer you should A apply Conservation of Energy B Conservation of Momentum Example 6 12c Tarzan M 80 kg swings on a 12 m vine by letting go from an angle of 60 degrees from the vertical At the bottom of his swing he picks up Jane m 50 kg To what angle do Tarzan and Jane swing To calculate Tarzan Jane s final height given the previous answer you should apply A Conservation of Energy B Conservation of Momentum Chapter 7 Rotational Motion Universal Law of Gravitation Kepler s Laws Angular Displacement Circular motion about a fixed AXIS Use polar coordinates r Distance r doesn t change Three possible units for Revolutions Degrees 1 …
View Full Document
Unlocking...