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Pip the Delivery Robot: Force Pairs in Hallway Bumps

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Pip the Delivery Robot: Force Pairs in Hallway Bumps

Use bump data and Newton's third law to find a mystery mass and design a safer robot.

Bumps with rolling carts

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

Robotics Team Notes: Pip Bumps Into Things

1The robotics team at Linwood Middle School built Pip, a small robot that carries library books and lab supplies between classrooms. With its tray, Pip has a mass of 6.0 kg. It rolls on smooth wheels and steers itself down the halls with a camera. In its first week on the job, Pip bumped into a rolling supply cart, a recycling bin and, once, a student's leg. No one was hurt, but coach Mr. Delroy Hutchins asked eighth graders Astrid Mensah and Joaquim Fairbanks to study the forces in a bump and to design a safer robot.

2First, the pair tested bumps with rolling carts on the smooth hallway floor. They loaded each cart with books to a measured mass. With its standard rubber bumper, Pip drove straight into the resting cart at 0.8 m/s. A switch in the bumper cut Pip's motors the moment it touched anything, so during each bump the only strong sideways pushes on Pip and the cart came from each other. A thin force sensor behind Pip's bumper recorded the largest force on Pip during the bump, called the peak force. A phone filmed each bump from the side, next to a meter stick, so the pair could find how much each object's speed changed. Each bump was repeated three times, and Table 1 shows the averages. In every bump, Pip either kept rolling forward more slowly or stopped. The pair also bumped Pip into Cart X, a cart of library returns whose mass they did not know.

3Next, the pair tested hallway safety with a shin dummy, a padded post bolted to the floor with a force sensor behind its padding. Pip drove straight into the dummy with different bumpers and top speeds (Table 2). Mr. Hutchins gave three criteria. The peak force on the dummy must be 65 N or less, so a bump would not hurt a person. Pip's top speed must be 0.5 m/s or more, so deliveries finish between classes. With its bumper, Pip must be 60 cm wide or less to fit through the gap beside the lab benches. The bumper wraps around the front corners, so it adds its thickness to both sides of Pip's 50 cm body.

4The school is also building a second robot, Quill, which has a mass of 12 kg. In narrow halls, the two robots could meet head-on.

Table 1. Pip (6.0 kg, 0.8 m/s) bumps a resting cart
CartCart mass (kg)Peak force on Pip (N)Pip's speed change (m/s)Cart speed change (m/s)
A2600.30.9
B3700.40.8
C6850.60.6
D121000.80.4
X?950.720.48
1.
Look at Carts A to D. Which pattern does Table 1 show?
Question 1 options
2.
Circle every statement about the bump with Cart D that is correct.

3.
In the bump with Cart A, the cart's speed changed 3 times as much as Pip's, even though they pushed on each other with forces of the same size. Which explanation fits the data best?
Question 3 options
4.
In bump C, the masses were equal and the speed changes were equal. In bump D, the cart had twice Pip's mass, and its speed changed half as much as Pip's. In bump X, Pip's speed changed 1.5 times as much as the cart's.

Use the same pattern. The mass of Cart X is about kg.

Designing a safer Pip

Use paragraph 3, Table 2 and the three criteria.

Table 2. Pip drives into the shin dummy
DesignBumperTop speed (m/s)Peak force on dummy (N)Width with bumper (cm)
AStandard rubber, 1 cm0.811052
BStandard rubber, 1 cm0.45552
CFoam, 3 cm0.87556
DFoam, 3 cm0.65656
EFoam, 7 cm0.84064
5.

Compare Designs A and B. With the same bumper, driving at 0.8 m/s gave a peak force times as large as driving at 0.4 m/s.

6.
Which design meets all three of Mr. Hutchins's criteria?
Question 6 options
7.
During a bump, a box of lab supplies on Pip's tray slides forward and hits the front wall of the tray. Which two forces form a third-law force pair?
Question 7 options

When Pip meets Quill

Use paragraph 4 and the pattern in Table 1.

8.
Pip (6.0 kg) rolls east at 0.5 m/s, and Quill (12 kg) rolls west at 0.5 m/s. Both motors cut off as they bump head-on. During the bump, Quill's speed changes by 0.5 m/s, so it stops.

Pip has half of Quill's mass, so Pip's velocity changes by about m/s.

9.
Pip started at 0.5 m/s east, and its velocity changes by more than that, toward the west. What does Pip do right after the bump?
Question 9 options
10.
Both robots still meet head-on at 0.5 m/s each. Which change would make Pip's velocity change less in the bump?
Question 10 options
11.
Joaquim says, "The sensor behind Pip's bumper only tells us the force on Pip. For people's safety we need a second sensor on the dummy." Astrid says, "One sensor is enough." Make a claim about who is right and about which design the team should use. Use evidence from Tables 1 and 2, and explain your reasoning with Newton's third law.