42. what is the law of conservation of energy?

43. what happens to the kinetic energy of an object as its potential energy increases?

44. what happens to the potential energy of an object as its kinetic energy decreases?

45. which has more gravitational potential energy (gpe) in each situation?

a. a 7 kg object resting on a 5 m shelf or a 10 kg object resting on the same shelf

b. a 4 kg object resting on a 4 m shelf or a 4 kg object resting on a 10 m high shelf

46. what is the total energy of an object with 25 j of kinetic energy and 25 j of potential energy?

47. what is the potential energy in a system with a total energy of 100 j and 45 j of kinetic energy?

48. determine if the examples below describe kinetic or potential energy, then identify the specific type of involved.

| example | kinetic or potential | specific type of e |
| ---- | ---- | ---- |
| a car battery is ready to start an engine | | |
| a person at the top of a roller coaster hill is about to drop down the track | | |
| a guitar string is plucked and makes a noise you can hear across the room | | |
| a microwave oven warms up a frozen meal by using invisible waves to excite water molecules | | |
| a person stretches a large spring and holds it taut to be able to launch a toy across the room | | |
| a beam of bright white light shines across a dark room. | | |

Question

42. what is the law of conservation of energy?

43. what happens to the kinetic energy of an object as its potential energy increases?

44. what happens to the potential energy of an object as its kinetic energy decreases?

45. which has more gravitational potential energy (gpe) in each situation?

a.  a 7 kg object resting on a 5 m shelf or a 10 kg object resting on the same shelf

b.  a 4 kg object resting on a 4 m shelf or a 4 kg object resting on a 10 m high shelf

46. what is the total energy of an object with 25 j of kinetic energy and 25 j of potential energy?

47. what is the potential energy in a system with a total energy of 100 j and 45 j of kinetic energy?

48. determine if the examples below describe kinetic or potential energy, then identify the specific type of involved.

| example | kinetic or potential | specific type of e |
| ---- | ---- | ---- |
| a car battery is ready to start an engine |  |  |
| a person at the top of a roller coaster hill is about to drop down the track |  |  |
| a guitar string is plucked and makes a noise you can hear across the room |  |  |
| a microwave oven warms up a frozen meal by using invisible waves to excite water molecules |  |  |
| a person stretches a large spring and holds it taut to be able to launch a toy across the room |  |  |
| a beam of bright white light shines across a dark room. |  |  |

Accepted Answer

### Question 42
# Brief Explanations:
The law of conservation of energy states that energy cannot be created or destroyed, only transformed from one form to another, and the total energy of an isolated system remains constant.
# Answer:
Energy cannot be created or destroyed, only transformed, and total energy in an isolated system is constant.

### Question 43
# Brief Explanations:
By the law of conservation of energy (assuming no non - conservative forces like friction), as potential energy (PE) of an object increases, kinetic energy (KE) decreases because the total mechanical energy $E = KE+PE$ remains constant (or changes in a way that an increase in PE is balanced by a decrease in KE).
# Answer:
Kinetic energy decreases (assuming total mechanical energy is conserved).

### Question 44
# Brief Explanations:
Using the law of conservation of mechanical energy ($E = KE + PE$), when kinetic energy (KE) of an object decreases, potential energy (PE) increases (assuming no non - conservative forces and total mechanical energy is conserved).
# Answer:
Potential energy increases (assuming total mechanical energy is conserved).

### Question 45
The formula for gravitational potential energy is $GPE=mgh$, where $m$ is mass, $g$ is acceleration due to gravity, and $h$ is height.

#### Part (a)
# Explanation:
## Step 1: Recall GPE formula
The formula for gravitational potential energy is $GPE = mgh$. Here, $g$ (acceleration due to gravity) and $h$ (height of the shelf) are the same for both objects.
## Step 2: Compare masses
We have two objects: one with mass $m_1 = 7\space kg$ and another with $m_2=10\space kg$. Since $GPE$ is directly proportional to mass ($GPE\propto m$ when $g$ and $h$ are constant), and $10\space kg>7\space kg$.
# Answer:
The 10 kg object resting on the same shelf has more gravitational potential energy.

#### Part (b)
# Explanation:
## Step 1: Recall GPE formula
The formula for gravitational potential energy is $GPE=mgh$. Here, $m = 4\space kg$ is the same for both objects, and $g$ (acceleration due to gravity) is also constant.
## Step 2: Compare heights
We have two heights: $h_1 = 4\space m$ and $h_2 = 10\space m$. Since $GPE$ is directly proportional to height ($GPE\propto h$ when $m$ and $g$ are constant), and $10\space m>4\space m$.
# Answer:
The 4 kg object resting on a 10 m high shelf has more gravitational potential energy.

### Question 46
# Explanation:
## Step 1: Recall total energy formula
The total mechanical energy $E$ of an object is the sum of its kinetic energy ($KE$) and potential energy ($PE$), i.e., $E=KE + PE$.
## Step 2: Substitute values
Given $KE = 25\space J$ and $PE=25\space J$, then $E=25 + 25$.
# Answer:
The total energy is $50\space J$.

### Question 47
# Explanation:
## Step 1: Recall total energy formula
The total mechanical energy $E$ of a system is given by $E = KE+PE$, where $KE$ is kinetic energy and $PE$ is potential energy. We can re - arrange this formula to solve for $PE$: $PE=E - KE$.
## Step 2: Substitute values
Given $E = 100\space J$ and $KE = 45\space J$, then $PE=100 - 45$.
# Answer:
The potential energy is $55\space J$.

### Question 48
We will analyze each example based on the definitions of kinetic energy (energy of motion) and potential energy (stored energy) and their specific types:

| Example | Kinetic or Potential | Specific Type of Energy |
|--|--|--|
| A car battery is ready to start an engine | Potential | Chemical Potential Energy (battery stores chemical energy which can be converted to electrical energy) |
| A person at the top of a roller coaster hill is about to drop down the track | Potential | Gravitational Potential Energy (due to height above the ground) |
| A guitar string is plucked and makes a noise you can hear across the room | Kinetic | Sound Energy (the vibrating string and the sound waves are in motion) |
| A microwave oven warms up a frozen meal by using invisible waves to excite water molecules | Kinetic | Electromagnetic Energy (microwaves are electromagnetic waves in motion, and the excited water molecules are in motion - also includes thermal energy which is kinetic at the molecular level) |
| A person stretches a large spring and holds it taut to be able to launch a toy across the room | Potential | Elastic Potential Energy (stored in the stretched spring) |
| A beam of bright white light shines across a dark room. | Kinetic | Electromagnetic Energy (light is an electromagnetic wave in motion) |

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QUESTION IMAGE

Question

Explanation:

Question 42

Answer:

Question 43

example	kinetic or potential	specific type of e
a person at the top of a roller coaster hill is about to drop down the track
a guitar string is plucked and makes a noise you can hear across the room
a microwave oven warms up a frozen meal by using invisible waves to excite water molecules
a person stretches a large spring and holds it taut to be able to launch a toy across the room
a beam of bright white light shines across a dark room.