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See Explanations....

Explanation:

NOTE => See attached graph.

1. 25-Turn Electromagnet

a. Strength of Batteries 1.5v vs 6.0v

6v:1.5v => 4:1 voltage ratio => That is, 6v battery is 4x voltage of 1.5v battery.

b. Ratio of Paperclips Picked Up

23clips(6v):6clips(1.5v) => 3.8clips(6v):1clip(1.5v)

That is, the 6 volt battery-EM picks up 3.8x more clips than the 1.5v battery-EM assuming constant number of coils given.

c. Empirical Relationship

From data given, an increase in voltage (V) produces a proportional increase in number of paperclips (C) picked up.  Such is a Direct Relationahip between #Clips Picked Up and Battery Voltage.

Thus, C ∝ V => C = kV => k = C/V

Therefore, for k₁ = k₂ => C₁/V₁ = C₂/V₂

2. 50-Turn Electromagnet

a. Ratio of turns between electromagnets.

50-Turn EM : 25-Turn EM => 2:1 ratio of turns between electromagnets

b. Ratio of Paperclips Picked UP

Between maximum voltage and minimum voltages for 50-Turn EM

=> 47 clips (6v) : 13 clips (1.5v) => 3.6:1 ratio...

That is, the 6v battery-EM, on the average, picks up 3.6x more clips than the 1.5v battery-EM given 50-Turn EM.

3. Doubling number of coils:

Doubling the number of coils, on the average, doubles the number of clips picked up by either electromagnet.

      Voltage              50-Turn EM      25-Turn EM     Pick Up Ratio

         1.5v                         13                       6                        2:1

         3.0v                        26                     12                        2:1

         4.5v                         31                    15.5                      2:1

         6.0v                         47                     23                      2:1  

4. Doubling Voltages:

Doubling voltage doubles the number of clips picked up by a given electromagnet regardless of the number of coils associated with magnet.

25-Turn EM          Voltage      Clips Pkd UP

                                1.5v                 6      

                                3.0v               12                

Double voltage => Doubles # clips picked up*

50-Turn EM          Voltage      Clips Pkd UP

                                1.5v                 13      

                                3.0v                26                

Double voltage => Doubles # clips picked up*

*Double Voltage => Double #clips picked up regardless of number of coil turns in electromagnet.

5.  Predicting number of clips for 7.5v battery-EM

Using linear trendline equations shown on attached graphs...

#clips 50-Turn EM = 7.1333V + 2.5 = 7.1333(7.5) + 2.5 ≅ 56 clips

#clips 25-Turn EM = 3.6333V + 0.5 = 3.6333(7.5) + 0.5 ≅ 27 clips

Overall => 2:1 ratio of clips between 50-Turn EM and 25-Turn EM

6. Slope values based upon trendline equations shown on attached graphs are ...

25 Turn EM => slope = 3.6333

50 Turn EM => slope = 7.1333

Approximately a 2x increase upon doubling the number of coils of electromagnet.

Predicting number of clips for 1V electromagnets:

#Clips (1volt) 25-Turn EM = 3.6333(1) + 0.5 = 3.6833 ≅ 4 clips

#Clips (1volt) 50-Turn EM = 7.1333(1) + 2.5 = 9.6333 ≅ 10 clips

Shows to be consistent with double #clips with double number of coil turns.

every chemical equation adheres to the law of conservation of mass, which states that matter cannot be created or destroyed. therefore, there must be the same number of atoms of each element on each side of a chemical equation.