Conservation of energy worksheet #1 | ASSIST - Free Printable

The zoomed-in view of point ③ confirms the labels for PE, KE, ME, v, and h. However, like the other points, the image is too blurry to extract any specific numerical values or text. Since I cannot read any pre-filled values from the image, I must solve the problem based on the principles of physics and the given information.

The key piece of information is the height at point ②, which is explicitly labeled as 1 meter. This allows me to calculate the potential energy at that point relative to the bottom (point ①).

To proceed, I will assume a standard value for the mass of the skateboarder, for example, $m = 50 \, \text{kg}$, and use $g = 9.8 \, \text{m/s}^2$ for calculations. I will also assume that the skateboarder starts from rest at point ①, which is a common assumption in such problems if not otherwise specified. If the skateboarder starts from rest, then the initial kinetic energy at point ① is zero, and all the mechanical energy is potential energy. However, since point ① is at the bottom, its potential energy is zero, so if the skateboarder is moving, they must have kinetic energy there.

Actually, looking at the diagram again, it seems more likely that the skateboarder is moving at point ①, as they are shown with motion lines. Therefore, I will assume that at point ①, the height $h = 0$, so $PE_1 = 0$. The total mechanical energy $ME$ will be equal to the kinetic energy at point ①, $KE_1$. At point ②, $h = 1 \, \text{m}$, so $PE_2 = mgh = mg \cdot 1$. At point ③, the skateboarder is at the highest point, so their velocity $v = 0$ (momentarily), which means $KE_3 = 0$, and all the mechanical energy is potential energy, $PE_3 = ME$.

Since mechanical energy is conserved, $ME = PE_1 + KE_1 = PE_2 + KE_2 = PE_3 + KE_3$.

At point ①: $h_1 = 0$, so $PE_1 = 0$. Let's denote the initial kinetic energy as $KE_1$. Then $ME = KE_1$.

At point ②: $h_2 = 1 \, \text{m}$, so $PE_2 = mg \cdot 1$. Then $KE_2 = ME - PE_2 = KE_1 - mg$.

At point ③: $v_3 = 0$, so $KE_3 = 0$. Then $PE_3 = ME = KE_1$. The height at point ③, $h_3$, can be found from $PE_3 = mgh_3 = KE_1$, so $h_3 = \frac{KE_1}{mg}$.

However, without knowing the initial kinetic energy $KE_1$ or the mass $m$, I cannot provide numerical values. The problem might expect symbolic answers or assume a specific initial condition.

Perhaps the problem intends for us to assume that the skateboarder starts with a certain amount of kinetic energy at point ①, and we need to express everything in terms of that. Alternatively, maybe the diagram implies that the skateboarder reaches a certain height at point ③, but that height is not labeled.

Given the lack of specific values, I will provide a general solution based on the conservation of energy principle.

Let's assume the skateboarder has an initial kinetic energy $KE_1$ at point ①, where $h_1 = 0$.

- Point ① (bottom):
- $h_1 = 0$
- $PE_1 = 0$
- $KE_1 = \text{initial kinetic energy}$
- $ME = PE_1 + KE_1 = KE_1$
- $v_1 = \sqrt{\frac{2KE_1}{m}}$

- Point ② (1 meter height):
- $h_2 = 1 \, \text{m}$
- $PE_2 = mg \cdot 1 = mg$
- $KE_2 = ME - PE_2 = KE_1 - mg$
- $ME = KE_1$ (conserved)
- $v_2 = \sqrt{\frac{2KE_2}{m}} = \sqrt{\frac{2(KE_1 - mg)}{m}}$

- Point ③ (top):
- $v_3 = 0$ (at the highest point, velocity is momentarily zero)
- $KE_3 = 0$
- $PE_3 = ME = KE_1$
- $ME = KE_1$ (conserved)
- $h_3 = \frac{PE_3}{mg} = \frac{KE_1}{mg}$

To provide a complete answer, I need to make an assumption about the initial kinetic energy. A common approach in such problems is to assume that the initial kinetic energy is sufficient to reach a certain height, or to express the answers in terms of the initial conditions.

Alternatively, perhaps the problem expects us to recognize that the total mechanical energy is constant and to fill in the blanks accordingly, without specific numbers.

Given the constraints, I will present the solution in a general form, using symbols.

Final Answer:

Based on the conservation of mechanical energy, the values at each point are as follows:

- At Point ① (bottom, h=0):
- $PE = 0$
- $KE = \text{Initial Kinetic Energy}$
- $ME = \text{Initial Kinetic Energy}$
- $v = \sqrt{\frac{2 \times \text{Initial Kinetic Energy}}{m}}$
- $h = 0$

- At Point ② (height = 1 m):
- $PE = mg \times 1 = mg$
- $KE = \text{Initial Kinetic Energy} - mg$
- $ME = \text{Initial Kinetic Energy}$
- $v = \sqrt{\frac{2(\text{Initial Kinetic Energy} - mg)}{m}}$
- $h = 1 \, \text{m}$

- At Point ③ (top, v=0):
- $PE = \text{Initial Kinetic Energy}$
- $KE = 0$
- $ME = \text{Initial Kinetic Energy}$
- $v = 0$
- $h = \frac{\text{Initial Kinetic Energy}}{mg}$

This solution assumes no energy loss due to friction or air resistance and that the initial kinetic energy is known or can be expressed symbolically. If a specific initial velocity or energy were provided, numerical values could be calculated.