Question

1. as the skateboarder rides back and forth…

a. describe how the maximum velocity changes.
b. describe how the maximum height changes.
part c – track playground ranking tasks (friction turned off)
make the track below in the playground tab. do the ranking tasks below assuming no friction.
note that a and g are equal heights.

1. rank the skateboarder positions a – g above in order of greatest potential energy to least potential energy. ties are possible.

greatest
least

1. rank the skateboarder positions a – g above in order of greatest kinetic energy to least kinetic energy. ties are possible.

greatest
least
after you rank, run the simulation in slow motion to see how you did!

Explanation:

Part 7a

Step1: Recall Energy Conservation

In a system with friction (implied as skateboarder rides, friction exists), mechanical energy (potential + kinetic) is not conserved. Energy is lost to friction (heat, sound, etc.). So total mechanical energy decreases over time.

Step2: Relate Velocity to Kinetic Energy

Maximum velocity occurs when kinetic energy is maximum (at lowest height, assuming no friction, but with friction, still, at lowest points). Since total mechanical energy decreases (as energy is lost to friction), the maximum kinetic energy (and thus maximum velocity, since \( KE = \frac{1}{2}mv^2 \), mass \( m \) constant) will decrease with each back - and - forth motion.

Step1: Recall Potential Energy Formula

Gravitational potential energy is given by \( PE = mgh \), where \( m \) is mass, \( g \) is acceleration due to gravity, and \( h \) is height.

Step2: Analyze Energy Loss and Height

As the skateboarder rides back and forth, energy is lost to non - conservative forces (friction). The total mechanical energy (potential + kinetic) decreases. At the maximum height, the skateboarder's kinetic energy is zero (momentarily at rest), so all mechanical energy is potential energy. Since total mechanical energy decreases, and \( PE = mgh \) ( \( m \) and \( g \) constant), the maximum height \( h \) must decrease with each back - and - forth motion.

Step1: Recall Potential Energy Formula

Gravitational potential energy \( PE=mgh \). Assuming the mass \( m \) of the skateboarder is constant and \( g \) (acceleration due to gravity) is constant, the potential energy is directly proportional to the height \( h \) (\( PE\propto h \)).

Step2: Determine Heights from the Graph

• From the graph, positions \( A \) and \( G \) are at the same (highest) height.
• Position \( E \) is at a height lower than \( A \) and \( G \) but higher than \( C \).
• Position \( C \) is at a height higher than \( D \) and \( F \) but lower than \( E \), \( A \), \( G \).
• Position \( D \) and \( F \): \( D \) and \( F \) are at the same (lower) height, and \( B \) is at the lowest height (ground level, \( h = 0 \) approximately).

So the order of greatest to least potential energy (based on height, since \( PE\propto h \)): \( A = G>E > C>D = F>B \)

Answer:

The maximum velocity decreases with each back - and - forth motion because mechanical energy is lost to friction (e.g., due to the skateboarder - track interaction, air resistance), so the maximum kinetic energy (and thus maximum velocity, since \( KE=\frac{1}{2}mv^{2}\)) decreases over time.

Part 7b