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8.3 Conservation of Momentum

- The direction of force and impulse is the same as it was in the case of (a).

- The force on the wall due to each ball is normal to the wall along the positive direction.

- The force is assumed to be constant over the time interval.
- The forces are not always constant.
- Even though the brief time intervals are considered, forces vary a lot.
- It is possible to find an average effective force that produces the same result as the time-varying force.
- The area under the curve is equal to the impulse or change in momentum between times.
- The area is the same as the area inside the rectangle.
- Both the actual and effective forces have the same impulses and effects.

- The areas under the curves are the same.

- The assumption of a constant force in the definition of impulse is the same as the assumption of a constant acceleration.
- Nature is described adequately without the use of math.

- It is important that the quantity is conserved.
- In the examples of Impulse and, large changes in momentum were produced by forces acting on the system of interest.

- Considering a sufficiently large system is the answer to this question.
- It is possible to find a larger system in which total momentum is constant even if the components of the system change.

- The Earth recoils because of the force applied to it through the goalpost.
- Earth's recoil is immeasurably small and can be neglected in any practical sense, but it is real because it is more massive than the player.

- The force of the collision is the only unbalanced force on each car.
- Car 1 slows down as a result of the collision, while car 2 speeds up.
- We will show that the two-car system remains constant.

- A car of mass moving with a velocity of bumps into another car of mass and speed.
- The first car slows down to a speed of and the second car goes up to a speed of.
- The total momentum of the two cars after the collision is the same as before, if you think about it.

- It seems obvious that the collision time is the same for both cars, but it is only true for objects traveling at ordinary speeds.
- It is necessary to modify the assumption for objects travelling near the speed of light.

- The total momentum of the two-car system is constant because of the changes in momentum.

- This result has validity beyond the one-dimensional case.
- It is possible to show that total momentum is conserved for any isolated system with any number of objects.

- It is possible to see that momentum is conserved for an isolated system by considering the second law of momentum.
- It is constant for an isolated system.

- The three length dimensions in nature are independent, and it is interesting to note that momentum can be changed in different ways along each dimensions.
- When there is no air resistance, the horizontal forces are zero and the momentum is unchanged.
- The net vertical force is not zero along the vertical direction.
- The total momentum of the projectile-Earth system is conserved if it is considered in the vertical direction.

- If air resistance is not very high, the horizontal component of a projectile's momentum is still conserved.
- The net external horizontal force is still zero because the forces causing the separation are internal to the system.

- The net vertical force of the momentum is not zero.
- The space probe-Earth system needs to be considered in the vertical direction.
- If the separation did not happen, the center of mass of the space probe would be the same.

- The principle can be applied to a comet striking Earth and a gas with a lot of atoms.
- The net external force cannot be zero.
- The source of the external force can always be included in a larger system in which momentum is conserved.
- In a collision of two cars, the two-car system conserves momentum while the one-car system does not.

- Some aquatic animals are based on the principles of momentum.
- A jellyfish fills its umbrella section with water and then pushes the water out, causing it to move in the opposite direction to the water.
- Unlike jellyfish, squids are able to control the direction in which they move by aiming their nozzle forward or backward.
- squids can travel at speeds of 8 to 12 km/h.

- The BCG was used in the second half of the 20th century to study the strength of the heart.
- About once a second, your heart beats.
- Newton's third law states that a force in the opposite direction is exerted on the rest of your body.
- This reaction force can be measured with a ballistocardiograph.
- A moving table suspended from the ceiling can be used to measure this.
- The strength of the heart beat and the volume of blood passing from the heart can be gathered from this technique.

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