April 1, Week 11 Today: Chapter 8, Conservation of Momentum - PowerPoint PPT Presentation

April 1, Week 11 Today: Chapter 8, Conservation of Momentum Homework Assignment #8 - Due Monday, April 8 Mastering Physics: 8 problems from chapter 8 Written Questions: 8.101 Homework Assignment #9 - Due Friday, April 12. Exam #3 on Wednesday. Practice Exam available on webpage. Review session: Tuesday, April 2, 5:15-7:00 PM. Room 114 of Regener Hall. Momentum April 1, 2013 - p. 1/9

Using Conservation of Momentum II → − v B 2 B B − → v B 1 − → v A 1 A A − → v A 2 Before After M A − → v A 1 + M B − → v B 1 = M A − → v A 2 + M B − → v B 2 Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II → − v B 2 B B − → v B 1 − → v A 1 A A → − v A 2 Before After M A − → v A 1 + M B − → v B 1 = M A − → v A 2 + M B − → v B 2 Component Form: Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II − → v B 2 B B − → v B 1 − → v A 1 A A → − v A 2 Before After M A − → v A 1 + M B − → v B 1 = M A − → v A 2 + M B − → v B 2 Component Form: M A ( v A 1 ) x + M B ( v B 1 ) x = M A ( v A 2 ) x + M B ( v B 2 ) x Momentum April 1, 2013 - p. 2/9

Using Conservation of Momentum II − → v B 2 B B − → v B 1 − → v A 1 A A − → v A 2 Before After M A − → v A 1 + M B − → v B 1 = M A − → v A 2 + M B − → v B 2 Component Form: M A ( v A 1 ) x + M B ( v B 1 ) x = M A ( v A 2 ) x + M B ( v B 2 ) x M A ( v A 2 ) y + M B ( v B 2 ) y = M A ( v A 2 ) y + M B ( v B 2 ) y Momentum April 1, 2013 - p. 2/9

Collisions Collision - Any strong interaction that lasts a short period of time. Momentum April 1, 2013 - p. 3/9

Collisions Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Momentum April 1, 2013 - p. 3/9

Collisions Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Momentum April 1, 2013 - p. 3/9

Collisions Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy. Momentum April 1, 2013 - p. 3/9

Collisions Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy. Inelastic Collision - Conserves Momentum only. Momentum April 1, 2013 - p. 3/9

Collisions Collision - Any strong interaction that lasts a short period of time. Collisions are always assumed to conserve momentum because of the impulse hypothesis (The collision’s short duration and the large internal forces make the effect of external forces on the collision negligible.) Collisions are classified as to whether they also conserve kinetic energy. Elastic Collision - Conserves Momentum and Kinetic Energy. Inelastic Collision - Conserves Momentum only. Collisions may not conserve kinetic energy because they produce heat and/or the objects change shape upon collision. Momentum April 1, 2013 - p. 3/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B − → v B 1 − → v A 1 A Before Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B − → v B 1 − → v A 1 A Before M A − → v A 1 + M B − → v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B → − v B 1 − → v A 1 A Before After M A − → v A 1 + M B − → v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B B − → v B 1 − → v A 1 A A Before After M A − → v A 1 + M B − → v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B B − → v B 1 − → → − v A 1 v 2 A A Before After M A − → v A 1 + M B − → v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B B → − v B 1 − → → − v A 1 v 2 A A Before After ( M A + M B ) − → M A − → v A 1 + M B − → v 2 v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B B − → v B 1 − → → − v A 1 v 2 A A Before After ( M A + M B ) − → M A − → v A 1 + M B − → = v 2 v B 1 Momentum April 1, 2013 - p. 4/9

Perfectly Inelastic Collisions When the colliding objects stick together, the collision is called perfectly inelastic or a plastic collision. B B − → v B 1 − → − → v A 1 v 2 A A Before After ( M A + M B ) − → M A − → v A 1 + M B − → = v 2 v B 1 M A ( v A 1 ) x + M B ( v B 1 ) x = ( M A + M B ) ( v 2 ) x Components: M A ( v A 1 ) y + M B ( v B 1 ) y = ( M A + M B ) ( v 2 ) y Momentum April 1, 2013 - p. 4/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 6 kg B EFORE Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ (b) 20 m/s at 225 ◦ Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ (b) 20 m/s at 225 ◦ (c) 40 m/s at 225 ◦ Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ (b) 20 m/s at 225 ◦ (c) 40 m/s at 225 ◦ (d) 10 m/s at 135 ◦ Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ (b) 20 m/s at 225 ◦ (c) 40 m/s at 225 ◦ (d) 10 m/s at 135 ◦ (e) 40 m/s at 135 ◦ Momentum April 1, 2013 - p. 5/9

2D Conservation Exercise A 6 kg box-shaped firecracker explodes into two unequal pieces. If the first piece of mass 2 kg has velocity 20 m/s at 45 ◦ , what speed and direction must the other piece have? 20 m/s 6 kg 45 ◦ 2 kg B EFORE A FTER (a) 10 m/s at 225 ◦ (b) 20 m/s at 225 ◦ (c) 40 m/s at 225 ◦ (d) 10 m/s at 135 ◦ (e) 40 m/s at 135 ◦ � M A � � 2 � 0 = M A − → v A 2 + M B − → v B 2 ⇒ − → − → → − v B 2 = − v A 2 = − v Af M B 4 Momentum April 1, 2013 - p. 5/9