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Newton's Second Law

5,564 bytes added, 16:16, 23 November 2019
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<math>F=ma</math>
Where:
<math>F </math> = The [[Resultant Force]] on the [[object]].
<math>m </math> = The [[mass]] of the [[object]].
<math>a </math> = The [[acceleration]] of the [[object]].
===Example Calculations===
====Finding the Force given Mass and Acceleration====
{| class="wikitable"
| style="height:20px; width:200px300px; text-align:center;" |A 2.3kg [[object]] [[accelerate]]s at a rate of 8.8m/s/s. Calculate the [[Resultant Force|resultant force]] acting on the [[object]] correct to two [[Significant Figures|significant figures]].| style="height:20px; width:200px300px; text-align:center;" |A 5.5x10<sup>4</sup>kg rocket [[accelerate]]s at a rate of 61m/s/s. Calculate the [[Resultant Force|resultant force]] acting on the rocket correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 2.3kg
a = 8.8m/s/s
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 5.5x10<sup>4</sup>kg
a = 61m/s/s
|-
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>F=ma</math>
<math>F \approx 20N</math>
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>F=ma</math>
|}
====Finding the Acceleration given Mass and Force====
{| class="wikitable"
| style="height:20px; width:200px300px; text-align:center;" |A 7kg [[object]] is subjected to a [[Resultant Force|resultant force]] of 53N. Calculate the [[acceleration]] of the [[object]] correct to two [[Significant Figures|significant figures]].| style="height:20px; width:200px300px; text-align:center;" |A 160g snooker ball experiences a [[Resultant Force|resultant force]] of 12N. Calculate the [[acceleration]] of the snooker ball correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 7kg
F = 53N
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 160g = 0.16kg
F = 12N
|-
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>F=ma</math>
<math>53=7a</math>
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>F=ma</math>
<math>12=0.16a</math>
|-
| style="height:20px; width:200px300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>a = \frac{53}{7}</math>
<math>a \approx 7.6m/s/s</math>
| style="height:20px; width:200px300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>a = \frac{12}{0.16}</math>
<math>F=ma</math>
Where:
<math>F </math> = The [[Resultant Force]] on the [[object]].
<math>m </math> = The [[Inertial Mass]] of the [[object]].
<math>a </math> = The [[acceleration]] of the [[object]].
===Example Calculations===
====Finding the Force given Inertial Mass and Acceleration====
{| class="wikitable"
| style="height:20px; width:200px300px; text-align:center;" |A 1.23Mg [[object]] [[accelerate]]s at a rate of 5.3x10<sup>-2</sup>m/s/s. Calculate the [[Resultant Force|resultant force]] acting on the [[object]] correct to two [[Significant Figures|significant figures]].| style="height:20px; width:200px300px; text-align:center;" |A 1.7x10ng cell [[accelerate]]s at a rate of 320m/s/s. Calculate the [[Resultant Force|resultant force]] acting on the rocket correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 1.23Mg = 1230kg
a = 5.3x10<sup>-2</sup>m/s/s
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 1.7ng = 1.7x10<sup>-12</sup>kg
a = 320m/s/s.
|-
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>F=ma</math>
<math>F \approx 65N</math>
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers into the [[equation]] and [[Solve (Maths)|solve]].'''
<math>F=ma</math>
|}
====Finding the Acceleration given Inertial Mass and Force====
{| class="wikitable"
| style="height:20px; width:200px300px; text-align:center;" |A 9.2g [[object]] is subjected to a [[Resultant Force|resultant force]] of 3.7kN. Calculate the [[acceleration]] of the [[object]] correct to two [[Significant Figures|significant figures]].| style="height:20px; width:200px300px; text-align:center;" |A 333 tonne passenger plane experiences a [[Resultant Force|resultant force]] of 1.008MN. Calculate the [[acceleration]] of the passenger plane correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 9.2g = 0.0092kg
F = 3.7kN = 3700N
| style="height:20px; width:200px300px; text-align:left;" |'''1. State the known quantities'''
m = 333 tonne = 3.33 x 10<sup>5</sup>kg
F = 1.008MN = 1.008 x 10<sup>6</sup>N
|-
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>F=ma</math>
<math>3700=0.0092a</math>
| style="height:20px; width:200px300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>F=ma</math>
<math>1.008 \times 10^6 = (3.33 \times 10^5 )a</math>
|-
| style="height:20px; width:200px300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>a = \frac{3700}{0.0092}</math>
<math>a \approx 4.0 \times 10^5m/s/s</math>
| style="height:20px; width:200px300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>a = \frac{1.008 \times 10^6}{3.33 \times 10^5}</math>
<math>a \approx 3.0m/s/s</math>
|}
 
====Finding the Inertial Mass given the Force and Acceleration====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |An [[object]] is subjected to a [[Resultant Force|resultant force]] of 92N and [[accelerate]]s at a rate of 0.42m/s/s. Calculate the [[Inertial Mass|inertial mass]] of the [[object]] correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |The brakes of a car provide a [[force]] of 12kN and are able to [[decelerate]] it at a rate of 8.7m/s/s. Calculate the [[Inertial Mass|intertial mass]] of the car correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
a = 0.42m/s/s
 
F = 92N
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
 
a = 8.7m/s/s
 
F = 12kN = 12 x 10<sup>3</sup>N
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>F=ma</math>
 
<math>92=0.42m</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
 
<math>F=ma</math>
 
<math>12 \times 10^3 = 8.7m</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>m = \frac{92}{0.42}</math>
 
<math>m = 219.047619kg</math>
 
<math>m \approx 220kg</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>m = \frac{12 \times 10^3}{8.7}</math>
 
<math>m = 1379.31034kg</math>
 
<math>m \approx 1400kg</math>
|}
 
===References===
====AQA====
 
:[https://www.amazon.co.uk/gp/product/019835939X/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=019835939X&linkCode=as2&tag=nrjc-21&linkId=57e96876985fc39b1a3d8a3e3dc238b6 ''Newton’s Second Law of motion, pages 144-145, GCSE Physics; Third Edition, Oxford University Press, AQA '']
:[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Newton’s Second Law, pages 164, 165, GCSE Combined Science Trilogy; Physics, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Newton’s Second Law, pages 196, 197, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10102 ''Newton’s Second Law, pages 212, 214, GCSE Combined Science; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945598/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945598&linkCode=as2&tag=nrjc-21&linkId=ad276ad49df77ab4b40ab4fd0fe10103 ''Newton’s Second Law; investigating, page 214, GCSE Combined Science; The Revision Guide, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782946403/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782946403&linkCode=as2&tag=nrjc-21&linkId=32a0abb60dff015b15b50e9b1d7b4644 ''Newton’s Second Law; investigating, pages 167, 168, GCSE Combined Science Trilogy; Physics, CGP, AQA '']
:[https://www.amazon.co.uk/gp/product/1782945970/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945970&linkCode=as2&tag=nrjc-21&linkId=a120d24dcc7cc7a58192069a3aafc1d2 ''Newton’s Second Law; investigating, pages 199, 200, GCSE Physics; The Complete 9-1 Course for AQA, CGP, AQA '']
 
====Edexcel====
 
:[https://www.amazon.co.uk/gp/product/1782945741/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945741&linkCode=as2&tag=nrjc-21&linkId=30da4f2178da182547b62a7329d13b57 ''Newton’s Second Law, pages 149, 151, 154, GCSE Combined Science; The Revision Guide, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1782945733/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782945733&linkCode=as2&tag=nrjc-21&linkId=2a2dbec9db6bf5766c0458d908fa0a52 ''Newton’s Second Law, pages 16, 18, 21, GCSE Physics; The Revision Guide, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1292120223/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1292120223&linkCode=as2&tag=nrjc-21&linkId=068ecf40278c32406a7f1c6e66751417 ''Newton’s Second Law, pages 18-19, GCSE Physics, Pearson Edexcel '']
:[https://www.amazon.co.uk/gp/product/1292120193/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1292120193&linkCode=as2&tag=nrjc-21&linkId=572df39392fb4200db8391d98ae6314e ''Newton’s Second Law, pages 302-303, GCSE Combined Science, Pearson Edexcel '']
:[https://www.amazon.co.uk/gp/product/1782948163/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782948163&linkCode=as2&tag=nrjc-21&linkId=0fdbfd5dd397d6e24a9dfb250f08587f ''Newton’s Second Law, pages 35, 36, 46, GCSE Physics, CGP, Edexcel '']
:[https://www.amazon.co.uk/gp/product/1782948163/ref=as_li_tl?ie=UTF8&camp=1634&creative=6738&creativeASIN=1782948163&linkCode=as2&tag=nrjc-21&linkId=0fdbfd5dd397d6e24a9dfb250f08587f ''Newton’s Second Law; investigating, pages 39, 40, GCSE Physics, CGP, Edexcel '']
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