7. interpret the graphs by answering questions about energy
a. energy bar that stayed constant all the time: _______________
b. energy at a maximum when skater was at the top of the pipe: _______________
c. energy at a maximum when skater was at the bottom of the pipe _______________
d. energy that always stayed at zero: _______________
8. discuss the skater’s speed at different positions on the pipe
a. speed at top of pipe: _______________
b. speed at bottom of pipe: _______________
9. explain how the speed is connected to the energy values
_______________________________________________________

Question

Accepted Answer

### Question 7 (Interpreting Energy Graphs for a Skater on a Pipe)
#### Part a: Energy bar that stayed constant ALL THE TIME:
# Brief Explanations:
In a closed system (assuming no friction or air resistance, like in a physics simulation for a skater on a pipe), the total mechanical energy (sum of kinetic and potential energy) remains constant. So the total energy bar (total mechanical energy) should stay constant.
# Answer:
Total Mechanical Energy (or Total Energy, depending on the graph's labeling)

#### Part b: Energy at a maximum when skater was at the top of the pipe:
# Brief Explanations:
At the top of the pipe, the skater has maximum height. Gravitational potential energy ($PE = mgh$) depends on height ($h$). So potential energy (gravitational) is maximum here.
# Answer:
Gravitational Potential Energy

#### Part c: Energy at a maximum when skater was at the bottom of the pipe:
# Brief Explanations:
At the bottom of the pipe, the skater's height is minimum, so potential energy is low. But speed is maximum here. Kinetic energy ($KE=\frac{1}{2}mv^{2}$) depends on speed ($v$), so kinetic energy is maximum at the bottom.
# Answer:
Kinetic Energy

#### Part d: Energy that always stayed at zero:
# Brief Explanations:
If there's no friction (a common assumption in such idealized physics problems), thermal energy (due to friction) would be zero. Or if the system is defined without non - conservative forces, the energy associated with non - conservative work (like friction - related energy) is zero.
# Answer:
Thermal Energy (or Energy due to Friction, assuming no friction in the ideal case)

### Question 8 (Skater's Speed at Different Positions)
#### Part a: Speed at top of pipe:
# Brief Explanations:
At the top of the pipe, the skater has maximum potential energy (from $PE = mgh$) and minimum kinetic energy (from $KE=\frac{1}{2}mv^{2}$). Since kinetic energy is related to speed, a low kinetic energy means a low speed. In fact, at the very top (if we consider the extreme case of a perfect pipe and ideal conditions), the speed in the vertical direction might be zero (but horizontal speed could be non - zero, but in the context of a skater on a pipe, often we consider the speed related to the motion along the pipe; at the top, the skater is momentarily at rest or has minimum speed).
# Answer:
Minimum (or zero, in an idealized case with no horizontal motion component)

#### Part b: Speed at bottom of pipe:
# Brief Explanations:
At the bottom of the pipe, the skater has minimum potential energy and maximum kinetic energy (from $KE=\frac{1}{2}mv^{2}$). Since kinetic energy is directly related to the square of speed (for a given mass), maximum kinetic energy means maximum speed.
# Answer:
Maximum

### Question 9 (Connection between Speed and Energy Values)
# Brief Explanations:
Kinetic energy is given by the formula $KE = \frac{1}{2}mv^{2}$, where $m$ is the mass of the skater and $v$ is the speed. Potential energy (gravitational) is given by $PE=mgh$, where $h$ is the height. In a closed system (no energy loss), total mechanical energy $E_{total}=KE + PE$ is constant. When the skater is at the top of the pipe, $h$ is maximum, so $PE$ is maximum and $KE$ is minimum (so speed is minimum). When the skater is at the bottom of the pipe, $h$ is minimum, so $PE$ is minimum and $KE$ is maximum (so speed is maximum). As the skater moves from the top to the bottom, potential energy is converted into kinetic energy (increasing speed), and as the skater moves from the bottom to the top, kinetic energy is converted back into potential energy (decreasing speed).
# Answer:
Kinetic energy ($KE=\frac{1}{2}mv^{2}$) is directly related to speed ($v$). Higher speed means higher kinetic energy. Total mechanical energy ($KE + PE$, where $PE$ is potential energy) is constant (in an ideal system with no energy loss). At the top of the pipe, potential energy ($PE = mgh$) is maximum, so kinetic energy (and thus speed) is minimum. At the bottom, potential energy is minimum, so kinetic energy (and speed) is maximum. Energy is converted between kinetic and potential as the skater moves, with speed changing accordingly.

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Question

Explanation:

Question 7 (Interpreting Energy Graphs for a Skater on a Pipe)

Part a: Energy bar that stayed constant ALL THE TIME:

Answer:

Part b: Energy at a maximum when skater was at the top of the pipe: