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1D Collisions Unit A Momentum Objectives • You will be able to state and apply the Law of Conservation of Momentum to linear collisions. • You will be able to define isolated system, and be able to determine if a system is or is not isolated. Collisions and systems • A collision is an interaction between two objects where a force acts on each object for a period of time. • A group of two or more objects that interact is known as a system. • A system where the system’s mass is constant, and no external net force acts on the system is an isolated system. Momentum of a system… • … is defined as the sum of the momenta of all objects in the system. psys p A pB pC . . . The belief in the fact that momentum is conserved in all collisions has led to the Law of Conservation of Momentum. total p before collision total p after collision 1) mAv A mBvB mAv A mBvB Use when objects do not stick together. 2) mAv A mBvB mA mB v Use when objects stick together. 3) mAv A mBvB Use for explosions (momentum total is zero before). Note: These formulas are not on your formula sheets and you can use the first formula exclusively if you like. * Example: • Fred sits in a stationary, frictionless wheelchair and throws a 3.0 kg ball outward at 8.0 m/s. If the mass of Fred and his chair is 75 kg, what will be the velocity of Fred and the chair immediately after the ball is thrown? Solution • Before: • After mB 3.0kg mB 3.0kg vB zero vB f 8.0m / s mF 75kg mF 75kg vF zero vFf ?? psys zero Because both velocities are zero. Solution psysi psys f mB vB f psys f 0 vF f mF 0 pF f pB f 3.0kg 8.0m / s vF f pF f pB f 75m / s mF vFf mBvB f 0.32m / s [ R ] Example • A 50 g bullet is fired into a 650 g block of wood, which sits on a frictionless surface. After impact the bullet and block move right at 30 m/s. Find the bullet’s velocity just before impact. Solution • Before: • After mB 0.050kg mBW mB mW 0.700kg vBi ? vBW f 30m / s mW 0.650kg Because wood and vWi zero bullet move as a single object. pWi zero Solution mBW vBW f psysi psys f vBi mB pBi pWi pBW f 0.700kg 30m / s mvBi 0 mBW vBW f vBi 0.050kg 420m / s [ R ] 0.42km / s [ R ] Using “Conservation of Momentum” Colliding Objects Stick Together Example : A 1.50 g pellet is fired into a 12.3 g wood block. The block and imbedded pellet fly off at 2.78 m/s E. What was the pellet’s velocity before impact? mAv A mBvB mA mB v 0.00150 kg v A 0 0.00150 kg 0.0123 kg 2.78 m s 0.00150 kg v A 0 0.038364 kg m s v p 25.6 m E s Answer is “+” * Example 2: A 980 kg Toyota going at 52.8 km/h N collides with and becomes entangled with a 738 kg Honda going 79.3 km/h S. What is the velocity of the wreckage immediately after impact? Note: It does not matter what units of mass or velocity are used - just be consistent! mAv A mBvB mA mB v 980 kg 52.8 km 738 kg 79.3 km 980 kg 738 kg v' h h 51744 58523 1718 v' v ' 3.95 km S h Answer was “–” * Examples of “Explosion” Conservation of Momentum Problems Example : When a 960 g plate is dropped, the first 370 g piece flies off at 2.63 m/s S. What is the velocity of the second piece? mv mv 370 g 2.63 m 590 g v s v 1.65 m N s Note: In order for the total final momentum to be “0”, if one piece flies north, the other must fly south. * Example 2: What is the ratio of the velocities of the 3.46 g piece of an exploded firecracker to the other 5.96 g piece? mv mv 3.46 g v1 5.96 g v2 v1 5.96 v2 3.46 v1 1.72 x Note: The smaller piece has a velocity 1.72 times the velocity of the larger piece! *

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