Question

complete this review to check your understanding of the unit. use the diagram to answer questions 1–3. 1. at which point on the half-pipe track does the skater have the most potential energy? a. point a b. point b c. point c d. the skater’s potential energy is the same at all points on the track. 2. which of the following statements are true? choose all that apply. a. the skater’s potential energy decreases as he moves from point a to point c. b. the skater’s kinetic energy increases as he moves from point a to point c. c. the skater’s kinetic energy does not change as he moves from point a to point c. d. the skater has maximum potential energy at point c. 3. what eventually happens if the skater rides the half-pipe without adding energy to his skateboard by pushing with his feet? a. he will continue to move back and forth from one side to the other indefinitely. b. he will gradually come to a stop at point c. c. he will continue to move back and forth indefinitely but not all the way to the top of each ramp. d. he will come to an immediate stop at either point a or point c. use the chart to answer questions 4 and 5. 4. the information in the table can be used to calculate which of the following for each object? a. kinetic energy b. potential energy c. neither kinetic or potential energy d. both kinetic and potential energy 5. the kinetic energy / gravitational potential energy of an object is directly proportional to its mass and proportional to the square of its velocity. the kinetic energy / gravitational potential energy of an object is directly proportional to its mass and proportional to its height. an object may / may not have both kinetic energy and gravitational potential energy at the same time.

Explanation:

Question 1

Potential energy (PE) in a gravitational field is given by \( PE = mgh \), where \( m \) is mass, \( g \) is gravitational acceleration, and \( h \) is height. Higher height means more PE. Point A is the highest, so it has the most PE.

Question 2

• For A: As the skater moves from A (high) to C (low), height \( h \) decreases. Since \( PE = mgh \), PE decreases.
• For B: Total mechanical energy (ME) is conserved (ignoring friction for basic analysis). \( ME = PE + KE \). As PE decreases, KE (kinetic energy, \( KE=\frac{1}{2}mv^{2} \)) must increase (since speed increases as height drops).
• C is wrong because KE changes (speed changes). D is wrong because point C is the lowest (least PE).

Question 3

In reality, friction and air resistance act on the skater, converting mechanical energy to heat. Over time, energy is lost, so the skater’s maximum height on each side decreases until he stops at the lowest point (C, the bottom of the half - pipe) due to energy dissipation. A and C assume no energy loss (which is not real), and D is incorrect as he won’t stop immediately.

Question 4

Answer:

A. Point A