. Pause the simulation and raise the Blue Item up to 90°. What energy type is at its highest and why?

Answer 1

When you raise an object, such as a Blue Item, to a height of 90°, you are increasing its gravitational potential energy. The gravitational potential energy is at its highest when the object is at its maximum height because this form of energy is directly related to the position of the object in a gravitational field.

The reason for this is that gravitational potential energy is calculated using the formula:

\[ PE = mgh \]

where:

• \( PE \) is the potential energy,
• \( m \) is the mass of the object,
• \( g \) is the acceleration due to gravity, and
• \( h \) is the height above a reference point.

Since you are lifting the Blue Item to its highest point, its height \( h \) is maximized, thus maximizing its gravitational potential energy.

Answer 2

Play the simulation. Describe where the Blue Item is when it has reached its highest kinetic energy and what happens to the energy of the item as it gains height again.

Answer 3

In a typical simulation involving the motion of an object, such as the Blue Item, its kinetic energy is at its highest when it is moving the fastest. This usually occurs just before the object starts to change direction at the lowest point of its trajectory, assuming it is moving in a vertical path.

As the Blue Item is moving upward, it gains height, which causes its kinetic energy to decrease as some of that energy is converted into gravitational potential energy. Specifically:

1. Lowest Point (Highest Kinetic Energy): When the Blue Item is at its lowest point, it has maximum kinetic energy because it is moving rapidly due to the gravitational force acting on it. At this point, the gravitational potential energy is at its minimum (since height is lowest).

2. Gaining Height: As the Blue Item moves upward, its speed decreases due to the opposing force of gravity. This reduction in speed means that the kinetic energy is decreasing. Simultaneously, as the item rises, its height \( h \) increases, which results in an increase in gravitational potential energy.

As the Blue Item continues to gain height:

• Kinetic Energy (KE) decreases.
• Gravitational Potential Energy (PE) increases.

There is an energy transformation happening: the kinetic energy is being converted into gravitational potential energy. The total mechanical energy of the system remains constant (ignoring air resistance and other dissipative forces) as energy is conserved.

Once the Blue Item reaches its peak height, its kinetic energy will be at its lowest (approaching zero), and its gravitational potential energy will be at its maximum. From this peak position, if it begins to descend, the process will reverse, converting potential energy back into kinetic energy as it falls.

Answer 4

Continue to play the simulation. This simulation will go on and on for eternity if we let it. This simulation is in what we call a Closed System. We are only looking at the variables we want to in this simulation. In the Real World (Open System), if we had a Pendulum like this, it would eventually stop. Explain why it would stop in the Real World.

Answer 5

In a real-world scenario, a pendulum or any oscillating system will eventually come to a stop due to several factors that are not present in an ideal closed system, such as the one described in the simulation. In an open system like the real world, energy is lost over time due to various external influences, primarily friction and air resistance. Here are the key reasons why a pendulum would stop in the real world:

1. Air Resistance: As the pendulum swings, it moves through the air, which creates drag. This air resistance exerts a force opposite to the direction of the pendulum's motion, which slows it down and converts some of its kinetic energy into thermal energy, ultimately dissipating it into the environment.

2. Friction: Friction occurs at the pivot point of the pendulum where it is attached. This friction opposes the motion of the pendulum, causing energy to be lost as heat. Over time, this friction will gradually reduce the pendulum's swing amplitude.

3. Mechanical Inefficiencies: Any moving parts in the pendulum system, especially at the pivot, may have inefficiencies that can cause energy loss. For instance, if the pendulum's strings or rods create frictional forces, energy will be lost, further reducing the system's mechanical energy.

4. Thermal Energy: As energy is dissipated through air resistance and friction, it is transformed into thermal energy, which is transferred to the environment, resulting in a decrease in the energy available to maintain the pendulum's motion.

5. Initial Energy Losses: When the pendulum is set in motion, it is often released from a height. If there are any initial disturbances or imperfections in the release (like not releasing from a perfect height or angle), this can also cause immediate energy losses.

As a result of these factors, without a continual input of energy (like someone pushing the pendulum), the pendulum's motion will gradually diminish until it eventually comes to a complete stop. This is in contrast to the closed system of the simulation, where energy is conserved, allowing the pendulum to oscillate indefinitely without losing any energy.

Answer 6

A student drops a ball from three different heights, as shown. For each drop, she calculates what the kinetic energy of the ball would be when it hits the ground. The table shows her data.

The student says that a ball dropped from a height of 3.0 meters would have less than 96 joules of kinetic energy when it hits the ground. Is she correct and why?
Type Answer HERE:

She is correct because the higher the ball is dropped from, the less kinetic energy it will have when it hits the ground.
She is correct because the higher the ball is dropped from, the greater kinetic energy it will have when it hits the ground.
She is incorrect because the higher the ball is dropped from, the greater kinetic energy it will have when it hits the ground.
She is incorrect because the higher the ball is dropped from, the less kinetic energy it will have when it hits the ground.

Answer 7

The correct answer is:

She is incorrect because the higher the ball is dropped from, the greater kinetic energy it will have when it hits the ground.

Explanation:

The kinetic energy (KE) of an object just before it hits the ground is determined by its potential energy (PE) at the height from which it was dropped. The potential energy is given by the formula:

\[ PE = mgh \]

Where:

• \( m \) is the mass of the ball,
• \( g \) is the acceleration due to gravity (approximately 9.81 m/s²),
• \( h \) is the height.

When the ball is dropped, its potential energy is converted into kinetic energy as it falls. Therefore, the higher the ball is dropped from, the greater its potential energy at that height, and consequently, the greater its kinetic energy will be when it reaches the ground.

Thus, if the student dropped the ball from a height of 3.0 meters, it would indeed have greater kinetic energy when it hits the ground, not less. If the data in the table indicates that the kinetic energy at this height can reach or exceed 96 joules, then her assertion is incorrect.