Open Lab Saturday: Graphing the Energy of Balls, Bats and Runners

Read tables, pick the right graph shapes and compare kinetic energy in a sports science lab.

Station 1: the pitching machine

Read the lab notes and study Table 1. Use KE = ½ × m × v² when a question asks you to calculate.

Open Lab Saturday at the Sports Science Lab

1Every spring, the sports science lab at Cascade State University opens its doors to middle school students for Open Lab Saturday. Eighth grader Zainab Kirkland spent the morning with lab technician Dr. Leopold Arrieta at three stations that measure balls, bats and runners. Dr. Arrieta explained that a moving object has kinetic energy, the energy of motion. The lab finds it with the formula KE = ½ × m × v², where m is the mass in kilograms (kg) and v is the speed in meters per second (m/s), giving the energy in joules (J). The v² part means the speed multiplied by itself, so a speed of 20 m/s gives 20 × 20 = 400.

2At the first station, a pitching machine inside a net cage threw balls while the visitors watched from behind the net. Dr. Arrieta set the machine so that every ball left it at 20 m/s, and two light gates checked the speed of each throw. He fed it four kinds of balls with different masses: a tennis ball, a baseball, a softball and a heavy training ball. The lab's software worked out the kinetic energy of each throw, and Dr. Arrieta repeated every throw three times to make sure the speed held steady (Table 1).

3At the second station, a college hitter swung at the same 0.15 kg baseball resting on a batting tee, from an easy swing up to a full swing. A radar unit measured the exit speed, the speed of the ball as it left the bat. Zainab copied the exit speeds and energies into Table 2. Dr. Arrieta noted that a faster swing of the bat usually gives the ball a higher exit speed.

4At the third station, three student volunteers sprinted down a 30 m indoor lane. Each runner had been weighed on a lab scale before the run and had warmed up for ten minutes, and timing gates near the end of the lane measured each runner's top speed (Table 3). Before lunch, the group watched a college tennis player practice her serve on the court next door. The radar showed her 0.06 kg tennis ball leaving the racket at about 50 m/s.

Table 1: Pitching Machine (every ball at 20 m/s)
Ball	Mass (kg)	Speed (m/s)	Kinetic energy (J)
Tennis ball	0.06	20	12
Baseball	0.15	20	30
Softball	0.19	20	?
Training ball	0.3	20	60

Use the formula in paragraph 1 to find the missing value in Table 1.

The softball left the machine with J of kinetic energy.

Zainab graphs Table 1 with mass on the x-axis and kinetic energy on the y-axis. The graphs below show only the shape, not the exact numbers. Which shape matches Table 1?

Use Table 1. The training ball has 5 times the mass of the tennis ball.

At the same speed, the training ball had times the kinetic energy of the tennis ball.

Station 2: the batting tee

Study Table 2 and use paragraph 3 to answer the questions.

Table 2: Batting Tee (0.15 kg baseball)
Exit speed (m/s)	Kinetic energy (J)
10	7.5
20	30
30	?
40	120

Use the formula in paragraph 1 to find the missing value in Table 2. Do not round.

At an exit speed of 30 m/s, the baseball had J of kinetic energy.

Now Zainab graphs Table 2 with exit speed on the x-axis and kinetic energy on the y-axis. Which shape matches Table 2?

Use Table 2 and your answer to question 4. Speeding up from 10 m/s to 20 m/s added 22.5 J of kinetic energy. Do not round.

Speeding up from 30 m/s to 40 m/s added J of kinetic energy.

Station 3: the sprint lane, and putting it together

Study Table 3 and use the lab notes and all three tables to answer the questions.

Table 3: Sprint Lane Top Speeds
Runner	Mass (kg)	Top speed (m/s)
Wen	45	8
Marcus	80	5
Femi	60	7

Which runner in Table 3 had the most kinetic energy at top speed?

A. Marcus, with about 2,000 J
B. Wen, with about 1,440 J
C. Femi, with about 1,470 J
D. Marcus, with about 400 J

Marcus wants the same kinetic energy that Wen had at her top speed.

With his mass of 80 kg, Marcus would need to run at m/s.

The softball from the pitching machine had 38 J of kinetic energy. Circle each ball below that had more kinetic energy than that softball.

The 0.06 kg tennis ball served at 50 m/sThe 0.15 kg baseball hit off the tee at 20 m/sThe 0.30 kg training ball pitched at 15 m/sThe 0.15 kg baseball hit off the tee at 30 m/sA 0.06 kg tennis ball pitched at 30 m/s

10.

A parent visiting the lab says, "The heavier ball carries more energy every time, so the training ball is the ball that hits hardest in this whole lab." Do you agree? Write a claim, give evidence from Table 1 and paragraph 4 with at least one calculation, and explain your reasoning about how mass and speed each affect kinetic energy.