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Linear Momentum

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Linear Momentum. Vectors again. Review. Equations for Motion Along One Dimension. Review. Motion Equations for Constant Acceleration. 1. 2. 3. 4. Review. 3 Laws of Motion If in Equilibrium If not in equilibrium Change in Motion is Due to Force Force causes a change in acceleration.

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linear momentum

Linear Momentum

Vectors again

  • Equations for Motion Along One Dimension
  • Motion Equations for Constant Acceleration
  • 1.
  • 2.
  • 3.
  • 4.
  • 3 Laws of Motion
  • If in Equilibrium
  • If not in equilibrium
  • Change in Motion is Due to Force
  • Force causes a change in acceleration
  • Work
  • Energy
  • Law of conservation of energy
  • Power
  • efficiency
  • If an 18 wheeler hits a car, what direction will the wreckage move?
  • What is the force between the 18 wheeler and the car?
  • Newtons 2nd law
  • Linear momentum
  • SI
  • Newton defined it as quantity of motion
  • When an object collides with another, the forces on the object will momentarily spike before returning back to zero.
  • We now define impulse, J, as the change in momentum of a particle during a time interval
  • SI unit
  • A ball with a mass of 0.40 kg is thrown against a brick wall. It hits the wall moving horizontally to the left at 30 m/s and rebounds horizontally to the right at 20 m/s. (a) find the impulse of the net force on the ball during the collision with the wall. (b) If the ball is in contact with the wall for 0.010s, find the average horizontal force that the wall exerts on the ball during impact.
conservation of momentum
Conservation of Momentum
  • If a particle A hits particle B
conservation of momentum1
Conservation of Momentum
  • If there are no external forces acting on the system
conservation of momentum2
Conservation of Momentum
  • Change in momentum over time is zero
  • The sum of momentums is constant
conservation of momentum3
Conservation of Momentum
  • If there are no external forces acting on a system, Total Momentum of a system conserved
example recoil
Example - Recoil
  • A marksman holds a rifle of mass 3.00 kg loosely such that it’ll recoil freely. He fires a bullet of mass 5.00g horizontally with velocity relative to the ground of 300 m/s. What is the recoil velocity of the rifle?
example 2d example
Example – 2D example
  • Two battling robots are on a frictionless surface. Robot A with mass 20 kg moves at 2.0 m/s parallel to the x axis. It collides with robot B, which has a mass of 12 kg. After the collision, robot A is moving at 1.0 m/s in a direction that makes an angle α=30o. What is the final velocity of robot B?
conservation of momentum and energy
Conservation of Momentum and Energy
  • Elastic Collisions – Collisions where the kinetic energies are conserved. When the particles are in contact, the energy is momentarily converted to elastic potential energy.
conservation of momentum and energy1
Conservation of Momentum and Energy
  • Inelastic Collisions – collisions where total kinetic energy after the collision is less than before the collision.
  • Completely Inelastic Collisions- When the two particles stick together after a collision.
  • Collisions can be partly inellastic
completely inelastic collisions
Completely Inelastic Collisions
  • Collisions where two objects will impact each other, but the objects stick together and move as one after the collision.
completely inelastic collisions1
Completely Inelastic Collisions
  • Momentum is still conserved
  • Find v in terms of v0
completely inelastic collisions2
Completely Inelastic Collisions
  • Assume Particle B is initially at rest
completely inelastic collisions3
Completely Inelastic Collisions
  • Kinetic Energy

If B is at rest

examples young and freedman 8 37
Examples – Young and Freedman 8.37
  • At the intersection, a yellow subcompact car with mass travelling 950 kg east collides with a red pick up truck with mass 1900 kg travelling north. The two vehicles stick together and the wreckage travels 16.0 m/s 24o E of N. Calculate the speed of each of the vehicles. Assume frictionless.
problem ballistic pendulum
Problem – Ballistic Pendulum
  • The ballistic pendulum is an apparatus to measure the speed of a fast moving projectile, such as a bullet. A bullet of mass 12g with velocity 380 m/s is fired into a large wooden block of mass 6.0 kg suspended by a chord of 70cm. (a) Find the height the block rises (b) the initial kinetic energy of the bullet (c) The kinetic energy of the bullet and block.
problem ballistic pendulum1
Problem – Ballistic Pendulum
  • Velocity after impact
  • Kinetic energy after impact
problem ballistic pendulum2
Problem – Ballistic Pendulum
  • Kinetic energy after impact
  • Converted to potential at highest point
elastic collisions
Elastic Collisions
  • Momentum and Energy are conserved
  • Find v in terms of v0
elastic collisions one dimension
Elastic Collisions – One Dimension
  • If particle B is at rest
elastic collisions one dimension1
Elastic Collisions – One Dimension
  • If particle B is at rest
elastic collisions one dimension2
Elastic Collisions – One Dimension
  • If particle B is at rest
  • Substitute back
elastic collisions one dimension3
Elastic Collisions – One Dimension
  • If particle B is at rest
elastic collisions one dimension4
Elastic Collisions – One Dimension
  • If ma <<< mb
  • really small
  • In a game of billiards a player wishes to sink a target ball in the cornet pocket. If the angle to the corner pocket is 35o, at what angle is the cue ball deflected? (Assume frictionless)
  • Mass is the same
problem serway 9 36
Problem – Serway 9-36
  • Two particles with masses m and 3m are moving towards each other along the x axis with the same initial speeds. Particle m is travelling towards the left and particle 3m is travelling towards the right. They undergo an elastic glancing collision such that particle m is moving downward after the collision at right angles from initial direction. (a) Find the final speeds of the two particles. (b) What is the angle θ at which particle 3m is scattered.
elastic collisions and relative velocity
Elastic Collisions and relative velocity
  • In an elastic Collision, the relative velocities of the two objects have the same magnitude
young and freedman 8 42
Young and Freedman 8.42
  • A 0.150 kg glider (puck on an air hockey table) is moving to the right with a speed of 0.80 m/s. It has a head-on collision with a 0.300 kg glider that is moving to the left with velocity 2.20 m/s. Find the final velocities of the two gliders. Assume elastic collision.
problems young and freedman 8 12
Problems- Young and Freedman 8.12
  • A bat strikes a 0.145kg baseball. Just before impact the ball is travelling horizontally to the right at 50.0 m/s and it leaves the bat travelling to the left at an angle of 30o above the horizontal with a speed of 65.0 m/s. Find the horizontal and vertical components of the average force on the ball if the ball and bat were in contact for 1.75 ms.
giancoli 7 12
Giancoli 7-12
  • A 23 g bullet travelling at 230 m/s penetrates a 2.0kg block of wood and emerges cleanly at 170 m/s. If the wood is initially stationary on a frictionless surface, how fast does it move after the bullet emerges?
serway 9 28
Serway 9.28
  • A 90.0 kg full back running east with a speed 5.0 m/s is tackled by a 95.0kg opponent running north at 3.00 m/s. If the collision is completely inelastic, (a) find the velocity of the players just after the tackle. (b) find the mechanical energy lost during the collision.
prepare for pain
Prepare for pain
  • Giancoli 7-78
  • A 0.25kg skeet (clay target) is fired at an angle of 30o to the horizon with a speed of 25 m/s. When it reaches its maximum height, it is hit from below by a 15g pellet traveling vertically upwards at 200 m/s. The pellet is embedded into the skeet. (a) how much higher does the skeet go up? (b) how much further does the skeet travel?
assumptions so far
Assumptions so far
  • Objects approximated to be point particles
  • Objects only undergo translational motion
center of mass
Center of Mass
  • Real objects also undergo rotational motion while undergoing translational motion.
  • But there is one point which will move as if subjected to the same net force.
  • We can treat the object as if all its mass was concentrated on a single point
center of mass1
Center of Mass
  • Set an arbitrary origin point
  • Center of mass is the mass weighted average of the particles
  • A simplified water molecule is shown. The separation between the H and O atoms is d=9.57 x10-11m. Each hydrogen atom has a mass of 1.0 u and the oxygen atom has a mass of 16.0 u. Find the position of the center of mass.
  • For ease set origin to one of the particles
center of mass2
Center of Mass
  • 1) if there is an axis of symmetry, the center of mass will lie along the axis.
  • 2) the center of mass can be outside of the body
center of gravity
Center of Gravity
  • The point of an object which gravity can be thought to act.
  • This is conceptually different from center of mass
  • For now the center of gravity of an object is also it’s center of mass.
  • Center of mass computations useful for when mass of a system changes with time
  • James and Ramon are standing 20.0 m apart on a frozen pond. Ramon has a mass of 60.0 kg and James has mass of 90.0 kg. Midway between the two is a mug of their favourite beverage. They pull on the ends of a light rope. When James has moved 6.0 m how far has Ramon moved?

No external forces!

  • Center of Mass will not move!

Center of Mass will not move!

  • James moved 6m to the right
problem young and freedman 8 50
Problem – Young and Freedman 8.50
  • A 1200 kg station wagon is moving along a straight highway at 12.0 m/s. Another car with mass 1800kg and speed 20.0 m/s has its center of mass 40.0 m away. (a) Find the position of the center of mass of the two cars. (b) Find magnitude of total momentum of the system. (c) Find the speed of the center of mass of the system. (d) Find total momentum using center of mass.