Energy: Forms and Changes. 7th Grade Science Worksheets ... - Free Printable

The image shows a roller coaster track with a rider at different points, and the kinetic energy (KE) and potential energy (PE) are labeled at each position. The goal is to understand energy conservation and how it applies to the motion of the roller coaster.

Let’s analyze the situation step by step:

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Key Concepts:

- Kinetic Energy (KE): Energy due to motion.
$$
KE = \frac{1}{2}mv^2
$$
- Potential Energy (PE): Gravitational potential energy due to height.
$$
PE = mgh
$$
- Total Mechanical Energy (E):
$$
E = KE + PE
$$
- Conservation of Energy: In the absence of non-conservative forces (like friction or air resistance), total mechanical energy remains constant.

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Given Data at Each Point:

We'll label the points from left to right as A, B, C, D, E.

#### Point A (Top of the hill):
- Height = 100 m
- KE = 0 J
- PE = 50,000 J
- Total Energy = 0 + 50,000 = 50,000 J

#### Point B (Downhill, before valley):
- KE = 20,000 J
- PE = 30,000 J
- Total Energy = 20,000 + 30,000 = 50,000 J

#### Point C (Bottom of the valley):
- Height = 30 m (assumed from diagram)
- KE = 35,000 J
- PE = 15,000 J
- Total Energy = 35,000 + 15,000 = 50,000 J

#### Point D (Up next hill, 60 m high):
- KE = 20,000 J
- PE = 30,000 J
- Total Energy = 20,000 + 30,000 = 50,000 J

#### Point E (End, ground level):
- Height = 0 m
- KE = 50,000 J
- PE = 0 J
- Total Energy = 50,000 + 0 = 50,000 J

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Observations:

- At every point, total mechanical energy = 50,000 J.
- This confirms that energy is conserved — no energy is lost to friction or air resistance in this idealized model.
- As the roller coaster descends, potential energy converts to kinetic energy.
- As it climbs, kinetic energy converts back to potential energy.

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Task Interpretation:

Since you said “I uploaded an image with a task,” but didn’t specify the exact question, here are possible tasks and their solutions:

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✔ Possible Task 1: Verify Conservation of Energy

Answer:
Yes, total mechanical energy is conserved throughout the ride:
- All points have KE + PE = 50,000 J → Confirms energy conservation.

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✔ Possible Task 2: Find the mass of the rider/roller coaster

We can use data from Point A:
- PE = mgh = 50,000 J
- h = 100 m
- g ≈ 9.8 m/s²

$$
m = \frac{PE}{gh} = \frac{50,000}{9.8 \times 100} = \frac{50,000}{980} \approx 51.02\ \text{kg}
$$

So, the mass is approximately 51 kg (could be a person or small cart).

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✔ Possible Task 3: Determine if the roller coaster can reach the top of the second hill (60 m)

- The second hill is 60 m high.
- At the top of this hill, PE = mgh = 51.02 × 9.8 × 60 ≈ 30,000 J (matches given value).
- At that point, KE = 20,000 J → So it has enough energy to reach there.
- Since total energy (50,000 J) > PE at 60 m (30,000 J), yes, it can make it up.

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✔ Possible Task 4: What happens after point D?

- After point D, the roller coaster goes into a loop or drop.
- It reaches point E at ground level with all energy converted to KE (50,000 J).
- The path ends there, suggesting the ride finishes.

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✔ Conclusion:

This is a classic conservation of mechanical energy problem. The roller coaster starts with only potential energy at the top and converts it to kinetic energy as it moves down, then back to potential energy as it climbs. The total energy remains constant at 50,000 J, confirming no energy loss.

If your specific task was something else (e.g., calculating speed, finding height, or explaining energy transformation), let me know and I’ll tailor the answer!