Momentum and Collisions Physics 2053 Lecture Notes Momentum and Collisions

Momentum and Collisions Topics 6-01 Momentum and Impulse 6-02 Conservation of Momentum 6-03 Collisions Momentum and Collisions

Momentum and Impulse Momentum is a vector F m m A block moving with an initial velocity vi is acted on by a constant force F for a time Dt. A block of mass (m) is acted upon by a force (F) After a time (D) the block acquires a velocity vf Momentum is conserved Momentum is a vector Momentum and Collisions

Newton’s form of his 2nd law Momentum and Impulse Momentum and Impulse Newton’s 2nd Law p Using Calculus: Newton’s form of his 2nd law Momentum and Collisions

Momentum and Collisions Problem A 12 kg hammer strikes a nail at a velocity of 8.5 m/s and comes to rest in a time interval of 8.0 ms. (a) What is the impulse given to the nail? v m (b) What is the average force acting on the nail? Momentum and Collisions

Momentum and Collisions 07-01 The area under the curve on a Force versus time (F vs. t) graph represents A) impulse. B) momentum. C) work. D) kinetic energy. Momentum and Collisions

Conservation of Momentum Collision between to moving objects v1 u1 Fm = - FM M m FmDt = - FMDt FM Fm M m v = u Dpm = - DpM M m v2 u2 m(u2 - u1) = -M(v2 - v1) mu2 - m u1 = - Mv2 + Mv1 Conservation of Momentum: Blocks have the same speed (v) at closest approach. Mv1 + m u1 = Mv2 + mu2 Conservation of Momentum p(before) = p(after) Momentum and Collisions

Conservation of Momentum Collision with a stationary block before v after M m V = ? M m Using the conservation of momentum to find the final speed when two blocks stick together. Momentum and Collisions

Momentum and Collisions 07-08 A 9,300 kg boxcar traveling at 15.0 m/s strikes a second boxcar at rest. The two stick together and move off with a speed of 6.0 m/s. What is the mass of the second car? . Momentum and Collisions

Conservation of Momentum Bullet fired into a block which is initially at rest. after V before v M m mv (M + m)V Find the speed of the bullet and block after impact. Momentum and Collisions

Momentum and Collisions 07-01 A freight car moves along a frictionless level railroad track at constant speed. The car is open on top. A large load of coal is suddenly dumped into the car. What happens to the velocity of the car? A) It increases. B) It remains the same. C) It decreases. D) cannot be determined from the information given Momentum and Collisions

Elastic Collisions Inelastic Collisions Collisions Momentum and Kinetic Energy are both conserved Inelastic Collisions Only Momentum is conserved Elastic and Inelastic collisions A perfectly inelastic collision losses as much kinetic energy as possible Momentum and Collisions

An Inelastic Collision Collisions An Inelastic Collision before v1 v2 after m1 m2 vf m1 m2 Find the final speed after a Perfectly Inelastic Collision Momentum and Collisions

Momentum and Collisions 07-01 In an inelastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy? A) Kinetic energy is also conserved. B) Kinetic energy is gained. C) Kinetic energy is lost. D) none of the above Momentum and Collisions

Momentum and Collisions 07-01 Two objects collide and stick together. Kinetic energy A) is definitely conserved. B) is definitely not conserved. C) is conserved only if the collision is elastic. D) is conserved only if the environment is frictionless. Momentum and Collisions

Elastic Collision (General Equations) Collisions Elastic Collision (General Equations) mB mA vA1 vB1 mB mA vA2 vB2 General Equations for an elastic collision. Velocity is a vector - use + and - to indicate directions. Momentum and Collisions

Elastic Collision (vB1 = 0) Ball B is initially at rest. vA1 mA mB Collisions Elastic Collision (vB1 = 0) Ball B is initially at rest. vA1 mA mB mB mA vA2 vB2 Special Case: Elastic collision with m2 initially at rest. Momentum and Collisions

Elastic Collision (vB1 = 0 and mA= mB) Collisions Elastic Collision (vB1 = 0 and mA= mB) m vA1 m VB2 Special Case: Elastic collision with equal masses and with m2 initially at rest. Momentum and Collisions

Momentum and Collisions 07-01 In an elastic collision, if the momentum is conserved, then which of the following statements is true about kinetic energy? A) Kinetic energy is also conserved. B) Kinetic energy is gained. C) Kinetic energy is lost. D) none of the above Momentum and Collisions

Momentum and Collisions 07-01 When is kinetic energy conserved? A) in inelastic collisions B) in any collision in which the objects do not stick together C) in all collisions D) in elastic collisions Momentum and Collisions

Momentum and Collisions 07-01 When a light beach ball rolling with a speed of 6.0 m/s collides with a heavy exercise ball at rest, the beach ball's speed after the collision will be, approximately, A) 0. B) 3.0 m/s. C) 6.0 m/s. D) 12 m/s. Momentum and Collisions

Momentum and Collisions Problem Two billiard balls of equal mass undergo a perfectly elastic head-on collision. If one ball’s initial speed was 2.00 m/s and the other’s was 3.00 m/s in the opposite direction, what will be their speeds after the collision? Momentum and Collisions

Use conservation of momentum and energy. Collisions Ballistic Pendulum h Cons. Energy Cons. Momentum vo M m v Ballistic Pendulum Use conservation of momentum and energy. Momentum and Collisions

Collisions Ballistic Pendulum Find the speed of the bullet v M h m V Cons. Momentum v M m V Momentum and Collisions

Collisions Ballistic Pendulum M h V Cons. Energy Momentum and Collisions

Momentum and Collisions Problem A 28 g rifle bullet traveling 230 m/s buries itself in a 3.6 kg pendulum hanging on a 2.8 m long string, which makes the pendulum swing upward in an arc. Determine the vertical and horizontal components of the pendulum’s displacement. Momentum and Collisions

Momentum and Collisions Problem A bullet is fired vertically into a 1.40 kg block of wood at rest directly above it. If the bullet has a mass of 29.0 g and a speed of 510 m/s how high will the block rise after the bullet becomes embedded in it? Momentum and Collisions

Momentum and Collisions 07-01 Two objects collide and bounce off each other. Linear momentum A) is definitely conserved. B) is definitely not conserved. C) is conserved only if the collision is elastic. D) is conserved only if the environment is frictionless. Momentum and Collisions

Momentum and Collisions 07-01 A 100 kg football linebacker moving at 2.0 m/s tackles head-on an 80 kg halfback running 3.0 m/s. Neglecting the effects due to digging in of cleats, A) the linebacker will drive the halfback backward. B) the halfback will drive the linebacker backward. C) neither player will drive the other backward. D) this is a simple example of an elastic collision. Momentum and Collisions

Center of Mass (cm) xcm x1 x2 x y m2 m1 cm Momentum and Collisions

Location of the cm of the Earth-Moon system xcm mm me Center of Mass (cm) Location of the cm of the Earth-Moon system xcm mm me x Rm Momentum and Collisions

Momentum and Collisions Problem Find the center of mass of the three-mass system shown in the diagram. Specify relative to the left-hand 1.00 kg mass. x y 1.0 kg 1.5 kg 1.1 kg 0.5 m 0.25 m Momentum and Collisions

Momentum and Collisions 07-01 Consider two unequal masses, M and m. Which of the following statements is false? A) The center of mass lies on the line joining the centers of each mass. B) The center of mass is closer to the larger mass. C) It is possible for the center of mass to lie within one of the objects. D) If a uniform rod of mass m were to join the two masses, this would not alter the position of the center of mass of the system without the rod present. Momentum and Collisions

Momentum and Collisions 07-01 Two cars collide head-on on a level friction-free road. The collision was completely inelastic and both cars quickly came to rest during the collision. What is true about the velocity of this system's center of mass? A) It was always zero. B) It was never zero. C) It was not zero, but ended up zero. D) none of the above Momentum and Collisions

Total momentum of an isolated system of objects is conserved. Chapter 7 Summary Momentum : Impules: Newton’s second law: Total momentum of an isolated system of objects is conserved. Momentum is conserved during collisions. Momentum and Collisions

In an elastic collision, total kinetic energy is also conserved Chapter 7 Summary In an elastic collision, total kinetic energy is also conserved In an inelastic collision, some kinetic energy is lost. In a completely inelastic collision, the two objects stick together after the collision. The center of mass of a system is the point at which external forces can be considered to act. Momentum and Collisions

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