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Chapter 44: Internal and External Forces

- Consider a system of two blocks.
- The forces of impact would be the same if the blocks collide.
- The response to the forces would not be the same because of the different mass.
- The impact forces are internal in the absence of external forces acting on the objects.

- Both impulse and momentum are quantitive quantities.

- The "quantity of motion" discussed in his book was the product of an object's mass and speed.
- Linear momentum is a quantity with units of kilogram * meters per second.
- The letter p- is used to designate momentum.

- Consider the action of trying to change the motion of a moving object.
- The mass and the speed of the object are more important than the inertia of the object.
- A truck moving at a slow 1 meter per second can still cause a lot of damage because of it's mass.
- A small bullet, having a mass of 1 gram or less, does incredible damage because of its high speed.
- The damage is the result of a force of impact when something else intercepts the object.
- The nature of impact forces should be considered.

- A mass m moving with a velocity v in a frame of reference.
- The net force is the sum of all the forces and is responsible for changing the motion.

- The second law of motion is equivalent to this expression.

- This expression means that the net external force acting on an object is equal to the rate of change of momentum of the object and is an alternative form of the second law of motion.
- The net force applied is the same as the change in momentum.

- The impulse is a quantity that represents the effect of a force on a mass during a time interval.
- The impulse applied to an object is the same as the change in momentum of the object.

- A graph of force versus time is another way to consider impulse.

- The impulse in units of newton is measured under the curve.
- One way to view this concept is to see that the average force is 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609-

- A car is traveling at 20 m/s and stops for a while.

- The same impulse must be given to the car's passengers during the crash.
- The time interval over which the force is applied is shortened by the airbag.
- The curve has the same area under it.
- It is wider and not as high.

- Every action has an equal but opposite reaction according to the third law of motion.
- Whenever there is an interaction between two objects in the universe, there is a force reaction.
- Suppose we have two masses, m 1 and m 2, that are approaching each other along a horizontal surface.
- Let F-12 be the force that m 1 exerts on m 2, and let F-21 be the force that m 2 exerts on m 1 The forces must be equal and opposite according to the law.

- Rewriting this expression as F-12+F-21=0 leads to an interesting implication.

- The change in the sum of the momenta is zero, implying that the sum of the total momentum for the system is always the same.
- The law of conserved of linear momentum is what this conclusion is called.

- The total momentum before and after an interaction is the same in an isolated system.

- It is possible to extend the law of momentum to two or three dimensions.
- In both the horizontal and vertical directions, it is necessary to hold the momentum in the plane relative to the coordinate system.
- The standard techniques of vector analysis can be used to calculate these components.

- When there is a collision between two pieces of matter, momentum is always the same.
- The statement is not necessarily true about energy.
- The kinetic energy before and after a collision is not the same.
- The collision is described as elastic if the energy and momentum are the same.
- The collision is described as inelastic if the energy is not conserved after the collision.

- Imagine that a mass m has a velocity v- and is at rest along a horizontal surface.
- The two groups stick together.
- The total momentum before the collision must be equal to the total momentum after.
- The new mass of the system is M + m, and the new momentum is given by (m+M)u-.

- The system's energy is conserved in an elastic collision.

- The initial energy is 2.

- You may be asked to set up, but not solve, a system of equations on the AP Physics 1 exam.

- The second equation can be simplified.

- During elastic collisions, the characteristic "rebounding" can be observed.

- A mass of 2 kg is moving at a speed of 10 m/s along a horizontal surface.
- It collides, and sticks, with a mass moving in the same direction.

- The initial energy was lost in the collision.

- If the two objects collide completely inelastically, rank the magnitude of the momenta of the collision.

- Before the collision, sum the momenta of object A and object B.
- The absolute value total will be the highest after the collision since momentum is conserved.

- Crash D has the greatest loss of energy since all of it is lost in the collision.
- Crash D will release the most energy.

- The AP Physics 1 exam is not likely to have a calculation question that requires direct use of this formula, but you should understand the concepts.

- The center of mass is a useful concept.
- The center of mass is the point at which all the mass is balanced.
- The weighted average of all points of mass along each axis is what it is found by.

- The center of mass is where our forces are applied in our diagrams.
- The center of mass of an object is determined by the positions specified in our physics problems.
- An unsymmetrical object may not appear to travel in a parabola when undergoing projectile motion as it twists and turns during its flight.
- The center of mass is following the path.

- The overall momentum of a system of interacting particles obeys all of the laws of nature.
- A mass of gas consisting of many moving and interacting molecules can be modeled as being attracted to Earth by placing the total mass of the gas cloud at its center of mass.

- The quantity is equal to mv-.

- The area under a graph of force versus time is where the impulse is found.

- The change in momentum is equal to the change in impulse.

- The rate of change of momentum is equal to force.

- In an isolated system, the total momentum is not changed.

- The system's energy is conserved in an elastic collision.

- In an inelastic collision where mass stick together, the energy loss transforms into heat.

- In an isolated system, momentum is always maintained.
- If you read a problem that doesn't explicitly state that momentum is involved, you can assume that total momentum is conserved, and you should write the equations for that.
- Unless the collision is elastic, the energy is not necessarily conserved.

- Decide if there is an impact or a collision.
- If there is a collision, you should know whether it is elastic or inelastic.

- If the collision is inelastic, be sure to determine the new combined mass.

- If the collision is elastic, you should write the equations to conserve both momentum and energy.

- The change in momentum of a mass is equal to the impulse given to it.
- The change in momentum is the same as the net force.

- Remember the sign conventions for left, right, up, and down motions, and be sure to take into account any reversal of directions.

- If studied in the center-of-mass frame of reference, motions may be simpler.
- The motions of mass particles relative to the center of mass are considered in the frame.

- The center of mass will follow a smooth path after an internal explosion since the initial momentum in that frame was zero.
- The center of mass of the debris still follows the original trajectory if a projectile is launched at an angle.

- Two carts have masses of 1.5 and 0.7 kilogram and are held together by a massless spring.
- The cart moves to the left with a speed of 7 m/s.

- A ball with a mass of 0.15 kg has a speed of 5 m/s.
- It bounces off the wall with a speed of 3 m/s.

- A baseball is thrown at 35 m/s.
- The batter hits it with a high speed.

- An object is moving with a speed of 6 m/s to the right.
- It collides and sticks to an object moving with a speed of 3 m/s in the same direction.

- A mass moving with a speed of 7 m/s collides with a mass moving with a speed of 4 m/s.
- The mass has a new speed of 3 m/s after it reverses direction.

- A mass m is attached to a massless spring.
- The mass rests on the floor.
- The system is released after being compressed a distance from the spring's initial position.

- Two blocks are moving on a horizontal surface.
- The 1-kg block has a speed of 12 m/s, and the 4-kg block has a speed of 4 m/s, as shown in the diagram below.
- A massless spring is attached to the end of the block.
- The spring has a force constant of 1,000 N/m.

- A disk is at rest on a horizontal surface.
- It is hit by a disk with a speed of 4 m/s.
- The disk has a speed of 2 m/s after the collision.

- A girl is standing on a platform with wheels on a horizontal surface.
- The platform is attached to a massless spring with a force constant of 1,000 N/m.
- The girl throws a ball at an angle of 30 degrees to the horizontal.

- In a recoil the mass go in opposite directions.

- The rebound velocity is in the opposite direction.

- Since both objects are moving in the same direction, we can write (1)(6) + (2) (3) v '.
- The initial energy of the 1- kilo object is 18 J, while the initial energy of the 2- kilo mass is 9 J.
- The total initial energy is 27 J.
- After the collision, the object has a speed of 4 m/s and a final energy of 24 J.
- 3 J of energy has been lost.

- We write (2)(7),(4),(4),(4),(4),(4),(4) and get v ', which is 1 m/s.

- The mass is taken back under the radical sign so that we get p-xmk.

- For an instant, we have an inelastic collision.

- We get v-f=53.6 m/s when we solve for the final velocity.
- The initial values for the velocities are 72 J and 32 J for the blocks.
- The total initial energy is 104 J.
- We get a final energy of 78.4 J using the final velocity of 5.6 m/s and the combined mass of 5 kg.
- The spring is compressed by the difference in energy of the two objects.
- The maximum compression of the spring after the collision is calculated using the formula for the work done against it.

- If we treat the situation as elastic, we can use the initial velocities as a "before" condition for momentum and energy.
- After the rebound has taken place, we want to solve for the two final velocities of the blocks.
- To find both velocities, we need two equations, and we use the conserved of energy in this case to assist us.

- The known numbers are 28 v 1 f + 4 v 2 f and 208 v1f2+4v2f2.

- Only one of the two choices provides a meaningful set of solutions.
- The first mass has to rebound and its final velocity has to be negative.
- Our final answers are v 2 f and v 1 f.

- In the x -direction, we only have the initial momentum of the 0.1- kilogram disk with a speed of 4 m/s.
- The x-component of momentum given by (0.1)(2)cos 43 is the result of the collision.

- The disk has an unknown angle to the x- axis and has zero momentum.
- The x component will be positive and the y component negative if the angle is below the x axis.
- We will get a positive answer if our assumption is correct.
- A negative answer will let us know that the assumption is incorrect.
- The y component of final momentum is given by (0.4) v 2 f cos th.

- The ratio gives a tan of 0.535 and a th of 28deg.
- The final velocity for the disk is 0.72 m/s.

- The initial energy is found by using the data.
- The final data gives us a total final energy of 0.2 J.
- The amount of energy has been lost.

- The ball's velocities are 35 cos 30 and 30.31 m/s.
- (1)(30.31) is used to state that (1,050) v '.
- The recoil velocity of the platform-girl system can be expressed as v'-0.0289 m/s.

- The object's momentum is zero because it has zero velocity.

- An upward force is given to an object when it bounces.
- If it is large enough, it can be dangerous.

- If the mass is placed vertically onto the object, the increase in mass appears to lower the velocity since no force was acting in the direction of motion.
- Since the object did not have a horizontal motion, the energy from the moving object must act to accelerate the mass m. From the mass M frame of reference, it appears that the mass m is moving towards the object, slowing it down.

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