Question

exploration 1
analyzing potential energy
you may recall that potential energy is the energy an object has because of its position, ... (text about potential energy, pogo sticks)

1. the spring in a pogo stick stores energy in the system. match each description of the

spring in the pogo stick system with the state of energy in the system.
boxes: spring expands and applies force, spring reaches maximum expansion, spring is compressed by force, spring reaches maximum compression; and minimum elastic potential energy, maximum elastic potential energy, energy enters the system, energy leaves the system
energy in a system
we define the boundaries of a system to help us analyze a situation. energy can enter
or leave a system across its boundaries... (text about energy in pogo stick system)
energy transfers and transformations
if work is done on a system or by a system... (text about energy transfer, glass example)

1. look at the ramp system in the photo. what is

preventing the potential energy in this system
from being transformed into kinetic energy?
fields and potential energy
a field is any region in which a noncontact force has an effect... (text about gravitational, magnetic fields)

Explanation:

To solve the matching problem about the spring in a pogo - stick system and the state of energy in the system, we analyze each description:

1. "spring expands and applies force"

When the spring expands and applies a force, the elastic potential energy stored in the spring is converted into other forms of energy (like kinetic energy of the pogo - stick and the person). So, energy leaves the system.

2. "spring reaches maximum expansion"

At maximum expansion, the spring is at its least compressed (or stretched in a way related to its natural state for a pogo - stick spring). The elastic potential energy of a spring is given by the formula $U=\frac{1}{2}kx^{2}$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. At maximum expansion, the displacement from the equilibrium (compressed) position is minimum (close to zero). So, the elastic potential energy is at a minimum. Thus, "spring reaches maximum expansion" matches with "minimum elastic potential energy".

3. "spring is compressed by force"

When an external force compresses the spring, work is done on the spring. According to the work - energy theorem, the work done on the spring is stored as elastic potential energy, and energy is entering the system (the pogo - stick system). So, "spring is compressed by force" matches with "energy enters the system".

4. "spring reaches maximum compression"

Using the formula for elastic potential energy $U = \frac{1}{2}kx^{2}$, when the spring is at maximum compression, the displacement $x$ from the equilibrium position is maximum. So, the elastic potential energy $U$ is maximum. Thus, "spring reaches maximum compression" matches with "maximum elastic potential energy".

The correct matches are:

• spring expands and applies force $\longleftrightarrow$ energy leaves the system
• spring reaches maximum expansion $\longleftrightarrow$ minimum elastic potential energy
• spring is compressed by force $\longleftrightarrow$ energy enters the system
• spring reaches maximum compression $\longleftrightarrow$ maximum elastic potential energy

Answer:

To solve the matching problem about the spring in a pogo - stick system and the state of energy in the system, we analyze each description:

1. "spring expands and applies force"

When the spring expands and applies a force, the elastic potential energy stored in the spring is converted into other forms of energy (like kinetic energy of the pogo - stick and the person). So, energy leaves the system.

2. "spring reaches maximum expansion"

At maximum expansion, the spring is at its least compressed (or stretched in a way related to its natural state for a pogo - stick spring). The elastic potential energy of a spring is given by the formula $U=\frac{1}{2}kx^{2}$, where $k$ is the spring constant and $x$ is the displacement from the equilibrium position. At maximum expansion, the displacement from the equilibrium (compressed) position is minimum (close to zero). So, the elastic potential energy is at a minimum. Thus, "spring reaches maximum expansion" matches with "minimum elastic potential energy".

3. "spring is compressed by force"

When an external force compresses the spring, work is done on the spring. According to the work - energy theorem, the work done on the spring is stored as elastic potential energy, and energy is entering the system (the pogo - stick system). So, "spring is compressed by force" matches with "energy enters the system".

4. "spring reaches maximum compression"

Using the formula for elastic potential energy $U = \frac{1}{2}kx^{2}$, when the spring is at maximum compression, the displacement $x$ from the equilibrium position is maximum. So, the elastic potential energy $U$ is maximum. Thus, "spring reaches maximum compression" matches with "maximum elastic potential energy".

The correct matches are:

• spring expands and applies force $\longleftrightarrow$ energy leaves the system
• spring reaches maximum expansion $\longleftrightarrow$ minimum elastic potential energy
• spring is compressed by force $\longleftrightarrow$ energy enters the system
• spring reaches maximum compression $\longleftrightarrow$ maximum elastic potential energy