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Stadium Stairs and a Ball Toss: Height and Stored Energy

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Stadium Stairs and a Ball Toss: Height and Stored Energy

Model how the distance between an object and Earth changes stored energy.

The stair runs

Read the notes and Table 1, then answer the questions.

Open Day at the Sports Science Lab

1Each fall, the sports science lab at Brightwater University opens its doors to local middle schools. The lab studies how athletes move, from sprinters to basketball players. This year eighth graders Ottoline Baptiste and Kwame Esposito joined two stations, along with their physical education teacher, Mr. Ferdinand Oduya. At each station a lab assistant asked them to model how energy is stored as an athlete or a ball moves away from Earth and back again.

2The assistant explained that a runner and Earth pull on each other, so together they form a system. Energy is stored in this system, and the amount depends on the distance between the runner and Earth. The lab's software uses this rule: stored energy in joules (J) = mass in kilograms (kg) × 10 × height in meters (m).

3At the first station, each person ran up the stadium steps from the field and stopped at a numbered row. Each row is 0.4 m higher than the one below it. Ottoline climbed first, stopping at row 10 and then at row 20, while Kwame and Mr. Oduya each made one climb. A large screen beside the field showed the stored energy compared with the field (Table 1). A second screen at the concourse, a wide walkway level with row 10, showed the stored energy compared with the concourse instead. When Ottoline stood at row 20, the field screen read 4,000 J, but the concourse screen read 2,000 J.

4At the second station, a player tossed a 0.60 kg basketball straight up from her hands. A high-speed camera filmed the toss in front of a wall marked in centimeters, and the software worked out the ball's height above her hands and its speed in five frames (Table 2). The camera took hundreds of pictures each second, and the assistant picked five of them, from the moment the ball left the player's hands to the top of the toss. Air pushed on the ball so little that the lab ignored it.

5Before the students left, the assistant asked them to compare the two stations and to explain what the stair runs and the toss have in common. For each station, they also had to name the two objects that made up the system.

Table 1: Stair Runs (stored energy compared with the field)
RunnerMass (kg)Row reachedHeight above field (m)Stored energy (J)
Ottoline50104.02,000
Ottoline50208.04,000
Kwame60208.04,800
Mr. Oduya80156.0?
1.
Use the rule in paragraph 2 to find the missing value in Table 1.

At row 15, the system of Mr. Oduya and Earth stored J compared with the field.

2.
Which two runs in Table 1 should the students compare to see how the height alone changes the stored energy?
Question 2 options
3.
Use Table 1. Ottoline climbs from row 10 to row 20.

The energy stored in the system of Ottoline and Earth goes up by J.

4.
Use paragraph 3. At row 20, the field screen showed 4,000 J for Ottoline, but the concourse screen showed 2,000 J. Which explanation fits best?
Question 4 options

The ball toss

Use paragraph 4 and Table 2 to answer the questions.

Table 2: The 0.60 kg Basketball Toss
FrameHeight above hands (m)Speed (m/s)Kinetic energy (J)Stored energy (J)
A05.07.50
B0.454.04.82.7
C0.803.02.7?
D1.052.01.26.3
E: top of the toss1.25007.5
5.
Use the rule in paragraph 2 to find the missing value in Table 2. Do not round.

At frame C, the system of the ball and Earth stored J compared with the player's hands.

6.
Which statement best describes Table 2 as the ball rises from frame A to frame E?
Question 6 options
7.
Suppose the player tosses the same 0.60 kg ball harder, so that it rises 1.80 m above her hands. Use the rule in paragraph 2. Do not round.

At the top of this toss, the system of the ball and Earth stores J compared with her hands.

8.
At frame E the ball stops for an instant. Kwame says, "Right there the ball has no energy at all." Which response fits Table 2 best?
Question 8 options
9.
Sort each change by what happens to the energy stored in the system of the object and Earth.
10.
Ottoline writes in her notes: "At both stations, the farther the object got from Earth, the more energy was stored in the system of the object and Earth." Do you agree? Write a claim, give evidence from both tables, and explain your reasoning using the idea of a system. Then explain why the two screens in paragraph 3 showed different numbers.