Write a one sentence claim about the relationship between the battery voltage and the number of paperclips picked up. Use the data from the 25-turn electromagnet to guide you.
A group of students has been testing electromagnets in the lab. They made an electromagnet by wrapping copper wire around a nail. For one set of tests, they wrapped the wire around the nail 25 times. For the second set of tests, they wrapped the wire around the nail 50 times. They also have 8 different batteries: 1.5 V, 3.0 V, 4.5 V, 6.0 V, 7.5 V, 9.0 V, 10.5 V, and 12.0 V. They use their electromagnets to see how many paper clips each can pick up.
25-turn Electromagnet
Battery Voltage
Number of Paper Clips Picked Up
Average
First Trial
Second Trial
Third Trial
1.5 V
5
7
6
3.0 V
12
12
14
4.5 V
14
17
16
6.0 V
20
26
25
7.5 V
29
32
28
9.0 V
34
36
36
10.5 V
40
40
41
12.0 V
45
42
46
The higher the battery voltage, the greater the number of paper clips picked up by the 25-turn electromagnet.
Please state the relationship, identify the variables and incorporate data/trends/patterns for each variable in the sentence.
As the battery voltage increases from 1.5 V to 12.0 V, the number of paper clips picked up by the 25-turn electromagnet also increases, demonstrating a positive correlation between battery voltage and paper clip attraction in this particular configuration.
What is the approximate ratio of the number of paper clips picked up using the 6.0 V battery to the number picked up using the 3.0 V battery? Show your work.
To find the approximate ratio of the number of paper clips picked up using the 6.0 V battery to the number picked up using the 3.0 V battery, we find the average number of paper clips picked up for each:
For the 6.0 V battery:
(20 + 26 + 25) / 3 = 23.67
For the 3.0 V battery:
(12 + 12 + 14) / 3 = 12.67
Therefore, the ratio of the number of paper clips picked up using the 6.0 V battery to the number picked up using the 3.0 V battery is approximately 23.67 / 12.67, which is roughly 1.87:1.
round the answers to the nearest whole number, then make the ratio
After rounding the average number of paper clips picked up for each battery to the nearest whole number:
For the 6.0 V battery: 23
For the 3.0 V battery: 13
The ratio of the number of paper clips picked up using the 6.0 V battery to the number picked up using the 3.0 V battery is approximately 23:13.
Answer expressed as either a simplified whole number ratio or fraction, not a single digit:
The ratio of the number of paper clips picked up using the 6.0 V battery to the number picked up using the 3.0 V battery is 23:13, which simplifies to 23/13.
About how many times stronger than the 3.0 V battery is the 6.0 V battery? Show your work
To find out how many times stronger the 6.0 V battery is compared to the 3.0 V battery in terms of picking up paperclips, we can use the ratio of the number of paper clips picked up for each battery.
From the previous calculations, we had:
- Number of paper clips picked up using the 6.0 V battery: 23
- Number of paper clips picked up using the 3.0 V battery: 13
Dividing the number of paper clips picked up by the 6.0 V battery by the number picked up by the 3.0 V battery gives us:
23 / 13 ≈ 1.77
Therefore, the 6.0 V battery is approximately 1.77 times stronger than the 3.0 V battery in terms of picking up paper clips.
Write one sentence comparing these 2 values.
The 6.0 V battery is about 1.77 times stronger than the 3.0 V battery in terms of picking up paper clips.
What is the ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-coil electromagnet? Show your work.
50 turn
Battery Voltage
Number of Paper Clips Picked Up
Average
First Trial
Second Trial
Third Trial
1.5 V
10
16
11
3.0 V
28
24
31
4.5 V
30
32
36
6.0 V
44
50
42
7.5 V
57
51
50
9.0 V
68
78
69
10.5 V
80
76
76
12.0 V
91
90
92
To find the ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-turn electromagnet, we look at the average number of paper clips picked up for each:
For the 50-turn electromagnet:
Average = (10 + 16 + 11) / 3 = 12.33
For the 25-turn electromagnet:
Average = (23 + 13) / 2 = 18
The ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-turn electromagnet is approximately 12.33:18, which simplifies to 41:60.
the 25 turn is
25-turn Electromagnet
Battery Voltage
Number of Paper Clips Picked Up
Average
First Trial
Second Trial
Third Trial
1.5 V
5
7
6
3.0 V
12
12
14
4.5 V
14
17
16
6.0 V
20
26
25
7.5 V
29
32
28
9.0 V
34
36
36
10.5 V
40
40
41
12.0 V
45
42
46
Apologies for the previous error. Let's correct that calculation.
For the 25-turn electromagnet, the average number of paper clips picked up is as follows:
1.5 V: (5 + 7 + 6) / 3 = 6
3.0 V: (12 + 12 + 14) / 3 = 12.67
4.5 V: (14 + 17 + 16) / 3 = 15.67
6.0 V: (20 + 26 + 25) / 3 = 23.67
7.5 V: (29 + 32 + 28) / 3 = 29.67
9.0 V: (34 + 36 + 36) / 3 = 35.33
10.5 V: (40 + 40 + 41) / 3 = 40.33
12.0 V: (45 + 42 + 46) / 3 = 44.33
Therefore, calculating the ratio of the number of turns for the 50-turn electromagnet to the 25-turn electromagnet:
50-turn electromagnet average: 12.33
25-turn electromagnet average: 23.67
Ratio: 12.33 / 23.67 ≈ 0.52
The ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-turn electromagnet is approximately 0.52.
Please correct it for both the 50 turn and the 20 turns, I need to know the ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-coil electromagnet. Show step by step.
To find the correct ratio of the number of turns for the 50-turn electromagnet to the number of turns for the 25-turn electromagnet:
Calculate the average number of paper clips picked up for the 50-turn electromagnet:
50-turn electromagnet:
1.5 V: (10 + 16 + 11) / 3 = 12.33
3.0 V: (28 + 24 + 31) / 3 = 27.67
4.5 V: (30 + 32 + 36) / 3 = 32.67
6.0 V: (44 + 50 + 42) / 3 = 45.33
7.5 V: (57 + 51 + 50) / 3 = 52.67
9.0 V: (68 + 78 + 69) / 3 = 71.67
10.5 V: (80 + 76 + 76) / 3 = 77.33
12.0 V: (91 + 90 + 92) / 3 = 91
Calculate the average number of paper clips picked up for the 25-turn electromagnet:
25-turn electromagnet:
1.5 V: (5 + 7 + 6) / 3 = 6
3.0 V: (12 + 12 + 14) / 3 = 12.67
4.5 V: (14 + 17 + 16) / 3 = 15.67
6.0 V: (20 + 26 + 25) / 3 = 23.67
7.5 V: (29 + 32 + 28) / 3 = 29.67
9.0 V: (34 + 36 + 36) / 3 = 35.33
10.5 V: (40 + 40 + 41) / 3 = 40.33
12.0 V: (45 + 42 + 46) / 3 = 44.33
Now, calculate the ratio of the number of turns for the 50-turn electromagnet to the number of turns for the 25-turn electromagnet using their respective averages:
50-turn electromagnet average / 25-turn electromagnet average
= (12.33 + 27.67 + 32.67 + 45.33 + 52.67 + 71.67 + 77.33 + 91) / (6 + 12.67 + 15.67 + 23.67 + 29.67 + 35.33 + 40.33 + 44.33)
= 410.67 / 207.67
Therefore, the ratio of the number of turns of the 50-turn electromagnet to the number of turns of the 25-turn electromagnet is approximately 410.67:207.67, which can be simplified to approximately 1.98:1.
What does doubling the voltage from 3.0V to 6.0V do to the strength of the electromagnet?
This is a 5 point question and the point breakdown is:
1 pt for the claim
2 pts for the evidence
2 pts for connecting the claim to each piece of evidence
Claim: Doubling the voltage from 3.0V to 6.0V increases the strength of the electromagnet.
Evidence:
- For the electromagnet powered at 3.0V, the average number of paper clips picked up was 12.67.
- For the electromagnet powered at 6.0V, the average number of paper clips picked up was 23.67.
Connection:
- The evidence shows that when the voltage doubles from 3.0V to 6.0V, the average number of paper clips picked up by the electromagnet increases from 12.67 to 23.67.
- This increase in the average number of paper clips picked up directly correlates with the increase in voltage, indicating that the strength of the electromagnet is positively affected by doubling the voltage from 3.0V to 6.0V.
What does doubling the number of coils do to the strength of the electromagnet?
This is a 5 point question and the point breakdown is:
1 pt for the claim
2 pts for the evidence
2 pts for connecting the claim to each piece of evidence
Claim: Doubling the number of coils increases the strength of the electromagnet.
Evidence:
- For the electromagnet with 25 coils, the average number of paper clips picked up was 23.67.
- For the electromagnet with 50 coils, the average number of paper clips picked up was 27.67.
Connection:
- The evidence demonstrates that when the number of coils is doubled from 25 to 50, the average number of paper clips picked up increases from 23.67 to 27.67.
- This direct relationship between the increase in the number of coils and the increase in the average number of paper clips picked up supports the claim that doubling the number of coils enhances the strength of the electromagnet.