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7.3 Gravitational Potential Energy

- The package will rest once the person stops pushing.
- The package's energy can be negative until it has been removed.
- We can find the distance traveled after the person stops pushing by looking at the force of friction times the distance traveled and the angle between the force and displacement.

- The net force is calculated by canceling the normal force and force of gravity.
- The net 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- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- 888-609- To get the package to zero, the work must be minus the energy that the package started with and what the package accumulated due to pushing.
- Where is the distance to stop?

- This is a good distance for a package to travel on a conveyor system.
- The force in the opposite direction of motion is negative, so it removes the energy from the work.

- Some of the examples in this section can be solved without considering energy, but at the expense of missing out on gaining insights about what work and energy are doing in this situation.
- The solutions using energy are easier than those using dynamics alone.

- Lifting objects and climbing stairs is both scientific and everyday work.
- There is a transformation of energy when there is work.
- The work against the force goes into a form of stored energy that will be explored in this section.

- The force needed to lift the object is equal to its weight.
- The mass is being worked on.

- The state of separation between two objects is associated with this energy.
- We refer to this as the gained by the object, because we know that this energy is stored in the Earth's gravity.
- Potential energy is a property of a system, not a single object.
- An object's position relative to the surroundings within the Earth-object system has an effect on the object's potential to move.
- An external force is applied to the object.
- Positive work increases the potential energy of the system.
- We need a reference level for the potential energy to be equal to 0.
- We usually choose this point to be Earth's surface, but it's not important because the difference in potential energy is what relates to the work done.
- The first two rungs of a ladder will have the same amount of potential energy as the last two rungs.

- The potential energy can be converted to other forms of energy.
- If we release the mass, the force will do the same amount of work as it did on it, increasing its energy by the same amount.
- We can consider just the conversion of to without considering the intermediate step of work.
- It is easier to solve problems using energy than using forces.

- It is positive when the final height is greater than the initial height.

- The units of potential energy are the same as for work and other forms of energy.
- The mass is lowered as the clock runs.
- The mass can be thought of as gradually giving up its 4.90 J of potential energy without considering the force of gravity.

- The equation applies to any path that has a change in height, not just when the mass is lifted straight up.

- A simple multiplication is much easier to calculate than a complicated path.
- The double advantage of the idea of gravitational potential energy is that it makes calculations easier.
- We will consider any change in vertical position of a mass to be accompanied by a change in potential energy, and we will avoid the more difficult task of calculating work done by or against the force.

- The path does not affect the change in potential energy between points A and B.

- The work done by or against the force depends on the starting and ending points, not on the path between them.

- calculate the force on the knee joints if the person lands stiffly.

- The person's energy is brought to zero by the work done on him by the floor as he stops.
- The work done by the floor reduces the amount of energy in the air.

- The floor does negative work because it removes energy from the system.

- The person's knees are less than the height of the fall, so the additional change in energy during the knee bend is ignored.

- It's enough to break bones if the force is 500 times more than the person's weight.
- A better way to cushion the shock is to bend the legs or roll on the ground.
- The force of the bending motion is 100 times smaller than in the example.
- The method is shown in action.
- The shock in hopping is mitigated by the bending of the hind legs in each jump, which is the only large animal that does it.

- The work done by the ground reduces the kangaroo's energy as it lands.
- The impact on the bones is reduced by applying the force of the ground on the hind legs over a longer distance.

- The roller coaster's speed increases as gravity pulls it downhill.
- The roller-coaster-Earth system's potential energy is converted into energy.
- All work done by friction is converted to.

- As the roller coaster goes downhill, it loses energy.
- The normal force, which is parallel to the direction of motion, does not work because we neglect friction.
- The work on the roller coaster is done by gravity alone.
- The gain in energy from moving through a distance is equal to the loss in energy from moving downward.
- This can be written in an equation.

- The initial energy is zero.
- We will change this to show the minus sign clearly.

- There is initial energy in this case.

- The final energy is the sum of the initial energy and the potential energy.

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