Physics Week 8 notes
Physics Week 8 notes PHYS2001
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This 7 page Class Notes was uploaded by Grace Lillie on Sunday March 6, 2016. The Class Notes belongs to PHYS2001 at University of Cincinnati taught by Alexandru Maries in Fall 2016. Since its upload, it has received 27 views. For similar materials see College Physics 1 (Calculus-based) in Physics 2 at University of Cincinnati.
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Date Created: 03/06/16
Chapter 9 – Linear Momentum and Collisions 9.1 – Linear Momentum linear momentum: p=m⃗ v The time rate of change of the linear momentum of a particle is equal to dp the net force acting on the particle, or ∑ F= dt 9.2 – Analysis Model: Isolated System (Momentum) ptotonstant∆ p =tot =pi f When two or more particles in an isolated system interact, the total momentum of the system doesn’t change *The momentum of and isolated system is conserved, but the momentum of one particle in the system is not necessarily conserved. 9.3 – Analysis Model: Nonisolated System (Momentum) tf ⃗ ⃗ ∆ p=p fp = i ∫∑ F dt=I ti the impulse of the net force acting on a particle over the time interval Δt=t -t is a f i vector with a magnitude equal to the area under a force-time curve. It’s direction is the same as the direction of the change in momentum I= ( F ) ∆ t=∆⃗p ∑ avg impulse-momentum theorem—the change in the momentum of a particle equals the impulse of the net force acting on the particle impulse approximation—one of the forces exerted on a particle is assumed to act for a short time and is much greater than any other force present, and so replaces the net force in above equations e.g. when a baseball is hit with a bat, the contact force is much greater than the gravitational force, so the gravitational forces are ignored *used when the particle moves very little during the collision (p ind p f represent the momenta immediately before and after the collision) 9.4 – Collisions in One Dimension collision—an event during which two particles come close to each other and interact through forces. *momentum is conserved in any collision elastic collision—the total kinetic energy is conserved. Real-world collisions are only approximately elastic because kinetic energy may be lost due to sound (like when you play pool) and some deformation occurs. Perfect elastic collisions occur between atomic and subatomic particles. pf=p →i v +m1 1im v 2m 2i 1 1 f 2 2 f 1 1 1 1 K =K → m v +2 m v = m v + 2 m i f 2 1 1i 2 2 2i 2 1 1 f 2 2 When m is i2itially at rest: inelastic collision—total kinetic energy of the system is not conserved. perfectly inelastic—objects stick together after they collide ∆ p=0→ p =p →m v +m v =(m +m )v f i 1 1i 2 2i 1 2 f inelastic—when some kinetic energy is transferred away but the objects don’t stick together (like when a rubber ball bounces, energy is transformed when it is deformed when it hits) 9.5 – Collisions in Two Dimensions Break up the velocity vectors into x- and y-components using sine and cosine m 1 +1ix =m2v 2ixv 1 1 fx 2 2 fx m 1 1iym v2=m2iy 1 1 fy+m v2 2 fy 9.6 – The Center of Mass center of mass—a single point in a system used when describing the overall motion of a system. The translational motion of a system is as if the net external forced were applied to the center of mass. For example, if you balance a pencil on your finger at its center of mass and apply a force to either end, it will rotate. If you apply a force at the center of mass you will move the pencil in the direction of the force without any rotation. r = 1 ∫ ⃗dm The vector position of the center of mass:M M center of gravity—another special point. The net effect of the gravitational forces acting on each small mass element of an extended object is equivalent to the effect of a single force acting through this point. 9.7 – Systems of Many Particles ⃗ = 1∑ m v CM M ii ptot∑ m ii 1 ⃗ CM M ∑ m ii ∑ F =M a ⃗ ext CM The center of mass of a system of particles with a combined mass M moves like a single particle of mass M would under the influence of the net external force on the system 9.8 – Deformable Systems The equations in Section 9.7 also apply to the analysis of the motion of deformable systems 9.9 – Rocket Propulsion Vehicles like cars are propelled by the driving force of friction (i.e. the road on the car) and can be modelled as nonisolated systems with the impulse applied on the car by the roadway. Rockets in space are isolated systems in terms of momentum, with the system being the rocket and the ejected fuel. M i vf−v iv le where M is the mass of the rocket plus the fuel, and v is the e M f exhaust speed dv dM Thrust=M = v e dt | | dt thrust increases as the exhaust speed increases and as the rate of change of mass (burn rate) increases What’s Next . . . Chapter 10 – Rotation of a Rigid Object About a Fixed Axis 10.1 – Angular Position, Velocity, and Acceleration 10.2 – Analysis Model: Rigid Object Under Constant Angular Acceleration 10.3 – Angular and Translational Quantities 10.4 – Torque 10.5 – Analysis Model: Rigid Object Under a Net Torque 10.6 – Calculation of Moments of Inertia 10.7 – Rotational Kinetic Energy 10.8 – Energy Considerations in Rotational Motion 10.9 – Rolling Motion of a Rigid Object
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