Question

part 2 questions

1. state the independent and dependent variables. state anything that needs to be kept constant.

1. is the velocity at the bottom of the track directly proportional, inversely proportional,

proportional, or not proportional to the mass of the skater?

part 3 questions

1. make a scatter plot of velocity vs. starting height. this graph must have a title and axes must

be labeled with appropriate units. you can make the graph in excel, or on graph paper.

1. is velocity directly proportional, inversely proportional, proportional, or not proportional to

starting height?

part 4 questions

1. were the velocities different in part 4 compared to part 3? does this part violate the law of

conservation of energy? explain.

Explanation:

Question 7

To determine the relationship between velocity at the bottom of the track and the mass of the skater, we use the principle of conservation of mechanical energy (assuming no non - conservative forces like friction are considered for simplicity). The gravitational potential energy at the start ($U = mgh$) is converted into kinetic energy at the bottom ($K=\frac{1}{2}mv^{2}$). Setting $mgh=\frac{1}{2}mv^{2}$, we can cancel out the mass $m$ from both sides of the equation, getting $v = \sqrt{2gh}$. This shows that the velocity $v$ does not depend on the mass $m$ of the skater. So, the velocity at the bottom of the track is not proportional to the mass of the skater.

From the conservation of mechanical energy, $mgh=\frac{1}{2}mv^{2}$. Canceling mass $m$, we get $v=\sqrt{2gh}$. The velocity $v$ is related to the square root of the starting height $h$ ($v\propto\sqrt{h}$), not directly proportional (which would be $v\propto h$) or inversely proportional (which would be $v\propto\frac{1}{h}$) or just proportional (which would imply a linear relationship $v = kh$ for some constant $k$). So, velocity is not proportional (in the sense of direct, inverse, or simple proportionality) to the starting height.

1. Velocity Difference: If part 4 has different conditions (e.g., presence of friction, different track shape, etc.) compared to part 3, the velocities can be different. For example, if there is friction in part 4, some of the mechanical energy is converted into heat, so the kinetic energy (and thus velocity) at the bottom will be less than in part 3 where maybe friction was negligible.
2. Law of Conservation of Energy Violation?: The law of conservation of energy states that the total energy of an isolated system remains constant. If in part 4, there are non - conservative forces (like friction) acting, the mechanical energy (kinetic + potential) is not conserved, but the total energy (including energy lost to heat, sound, etc.) is still conserved. So, if the velocities are different, it does not violate the law of conservation of energy because the energy is just being transferred to other forms (like thermal energy) rather than being created or destroyed.

Answer:

Not proportional

Question 9