A student proposed the following hypothesis regarding electromagnetism: *Hypothesis*: The … — ACT

A student proposed the following hypothesis regarding electromagnetism:

*Hypothesis*: The magnetic field strength of an electromagnet, as measured by the number of steel paperclips it can lift, is directly proportional to the number of wire coils wrapped around its core.

To test this hypothesis, the student wrapped varying numbers of wire coils around an iron nail core, connected the coils to a constant power source, and recorded the average number of paperclips lifted over $5$ trials. The results are shown in the table below:

Number of wire coils	Average number of paperclips lifted
$10$	$4$
$20$	$8$
$30$	$12$
$40$	$13$
$50$	$13$

Which of the following modifications to the hypothesis is best supported by the experimental results?

A
The hypothesis is fully supported and requires no modification because the average number of paperclips lifted increases at a constant rate from $10$ coils to $50$ coils.
B
The hypothesis should be modified to state that the magnetic field strength decreases once the number of coils exceeds $30$ coils.
The magnetic field strength is directly proportional to the number of coils only up to $30$ coils, after which additional coils do not further increase the strength.Answer
D
The hypothesis should be modified to state that the magnetic field strength is inversely proportional to the number of coils across all tested values.

Answer

The magnetic field strength is directly proportional to the number of coils only up to

30

coils, after which additional coils do not further increase the strength.

The correct answer is correct because the ratio of paperclips to coils is constant at

0.4

from

10

30

coils, confirming a direct proportion in this range. However, at

40

and

50

coils, the number of paperclips lifted plateaus at

13

, indicating that wrapping more than

30

coils does not produce a proportional increase in magnetic strength.

Step-by-Step Solution

Analyze the student's initial hypothesis.

The hypothesis states that the number of paperclips lifted (representing magnetic field strength) is directly proportional to the number of wire coils. Mathematically, this means the ratio of paperclips to coils should remain constant.

Establishing the mathematical definition of direct proportionality allows us to test it against the data.

Calculate the ratio of paperclips lifted to wire coils for each data point in the table.

For

10

coils,

\frac{4}{10} = 0.4

. For

20

coils,

\frac{8}{20} = 0.4

. For

30

coils,

\frac{12}{30} = 0.4

. For

40

coils,

\frac{13}{40} = 0.325

. For

50

coils,

\frac{13}{50} = 0.26

Comparing these ratios identifies where the linear relationship holds and where it breaks down.

Identify the trend and determine how to modify the hypothesis.

The ratio is constant at

0.4

up to

30

coils, but it decreases at

40

and

50

coils as the average number of paperclips lifted plateaus at

13

. Thus, the direct proportionality is valid only up to

30

coils, and the hypothesis must be restricted to this range.

A modified scientific hypothesis must align with all observed experimental facts.

Key Concept

Formulating and Modifying Hypotheses

Question

Answer

Step-by-Step Solution

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