If her speed is 2.91 m/s at the lowest position, then what amount of energy is lost due to resistance forces?

To determine the amount of energy lost due to resistance forces when her speed is 2.91 m/s at the lowest position, we'll need to apply the principles of energy conservation, specifically focusing on kinetic energy and the work-energy principle.

1. Break Down the Problem

1. Identify the initial potential energy (PE) at a height before reaching the lowest position.
2. Calculate the kinetic energy (KE) at the lowest position using her speed.
3. Determine the energy lost due to resistance forces by subtracting the kinetic energy from the initial potential energy.

2. Relevant Concepts

• Potential Energy (PE) is given by the formula: $PE = mgh$ where $m$ is the mass, $g$ is the acceleration due to gravity (approximately $9.81 \, \text{m/s}^2$), and $h$ is the height.

• Kinetic Energy (KE) is given by the formula: $KE = \frac{1}{2} mv^2$ where $v$ is the speed.

3. Analysis and Detail

Assuming the mass $m$ and height $h$ are known, the steps are:

1. Calculate the Kinetic Energy at the lowest position: $KE = \frac{1}{2} mv^2 = \frac{1}{2} m (2.91)^2$

2. Calculate the Potential Energy at the height $h$: $PE = mgh$

3. The energy lost due to resistance forces (E_lost) is: $E_{lost} = PE - KE$

4. Verify and Summarize

To summarize, you need the values of $m$ and $h$ to compute $PE$ and finalize the energy lost calculation.

Final Answer

The final result for the energy lost due to resistance forces can be expressed as: $E_{lost} = mgh - \frac{1}{2} m (2.91)^2$ Please provide the values for $m$ (mass) and $h$ (height) to obtain a specific numerical answer.