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Created page with "==Key Stage 4 Higher== ===Meaning=== The law of '''conservation of momentum''' is the fact that the total momentum in a closed isolated system r..."
==Key Stage 4 Higher==
===Meaning===
The law of '''conservation of momentum''' is the fact that the total [[momentum]] in a [[Closed Isolated System|closed isolated system]] remains the same before and after an interaction.
===About Conservation of Momentum===
: '''Conservation of momentum''' means that if you add the [[momentum]] of every [[object]] before and event this will be the same as the total [[momentum]] after that event.
'''Conservation of momentum''' can be applied to 3 types of interaction to allow us to predict the outcome:
*Explosions - When two [[object]]s begin with zero [[momentum]] but are [[force]]d apart in opposite directions.
*Elastic Collisions - When two [[object]]s bounce off one another and the total [[Kinetic Energy Store|kinetic energy]] before a collision is the same as the total [[Kinetic Energy Store|kinetic energy]] after the collision.
*Inelastic Collisions - When [[Kinetic Energy Store|kinetic energy]] is lost during a collision, often with the [[object]]s sticking together to form a larger [[object]].
===Equation===
''NB: You do not need to remember the equation but you must be able to apply the law of '''conservation of momentum'''.''
Total Momentum Before = Total Momentum After
<math>p_{before} = p_{after}</math>
Where:
<math>p_{before}</math> = The total [[momentum]] before an interaction.
<math>p_{after}</math> = The total [[momentum]] after the interaction.
===Explosions===
: During an explosion a single [[object]] with zero [[momentum]] splits into two smaller [[object]s.
: The total [[momentum]] before the explosion is zero. Due to '''conservation of momentum''' the total [[momentum]] after the explosion is also zero.
<math>p_{before} = p_{after}</math>
Since:
<math>p = mv</math>
Then:
<math>0 = m_1 v_1 + m_2 v_2</math>
Where:
<math>m_1</math> = The [[mass]] of [[object]] 1.
<math>v_1</math> = The [[velocity]] of [[object]] 1 after the explosion.
<math>m_2</math> = The [[mass]] of [[object]] 2.
<math>v_2</math> = The [[velocity]] of [[object]] 2 after the explosion.
====Example Explosion Calculations====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |An 80kg ice skater and a 90kg ice skater begin at rest and then push away from one another. The 80kg ice skater moves away with a velocity of 0.45m/s. Calculate the [[velocity]] of the 90kg ice skater correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |An 18th century cannon of [[mass]] 2000kg fires a 5.5kg cannon ball at a [[velocity]] of 180m/s. Calculate the recoil [[velocity]] of the cannon correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
p<sub>before</sub> = 0kgm/s
m<sub>1</sub> = 80kg
m<sub>2</sub> = 90kg
v<sub>1</sub> = 0.45m/s
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
p<sub>before</sub> = 0kgm/s
m<sub>1</sub> = 2000kg
m<sub>2</sub> = 5.5kg
v<sub>1</sub> = 180m/s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>p_{before} = p_{after}</math>
<math>0 = m_1 v_1 + m_2 v_2</math>
<math>0 = 80 \times 0.45 + 90 \times v_2</math>
<math>0 = 36 + 90v_2</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>p_{before} = p_{after}</math>
<math>0 = m_1 v_1 + m_2 v_2</math>
<math>0 = 2000 \times v_1 + 5.5 \times 180</math>
<math>0 = 2000v_1 + 990</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>90v_2 = -36</math>
<math>v_2 = \frac{-36}{90}</math>
<math>v_2 = -0.40m/s</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>2000v_1 = -990</math>
<math>v_1 = \frac{-990}{2000}</math>
<math>v_1 = -0.495m/s</math>
<math>v_1 \approx -0.50m/s</math>
|}
===Elastic Collisions===
===Inelastic Collisions===
===Meaning===
The law of '''conservation of momentum''' is the fact that the total [[momentum]] in a [[Closed Isolated System|closed isolated system]] remains the same before and after an interaction.
===About Conservation of Momentum===
: '''Conservation of momentum''' means that if you add the [[momentum]] of every [[object]] before and event this will be the same as the total [[momentum]] after that event.
'''Conservation of momentum''' can be applied to 3 types of interaction to allow us to predict the outcome:
*Explosions - When two [[object]]s begin with zero [[momentum]] but are [[force]]d apart in opposite directions.
*Elastic Collisions - When two [[object]]s bounce off one another and the total [[Kinetic Energy Store|kinetic energy]] before a collision is the same as the total [[Kinetic Energy Store|kinetic energy]] after the collision.
*Inelastic Collisions - When [[Kinetic Energy Store|kinetic energy]] is lost during a collision, often with the [[object]]s sticking together to form a larger [[object]].
===Equation===
''NB: You do not need to remember the equation but you must be able to apply the law of '''conservation of momentum'''.''
Total Momentum Before = Total Momentum After
<math>p_{before} = p_{after}</math>
Where:
<math>p_{before}</math> = The total [[momentum]] before an interaction.
<math>p_{after}</math> = The total [[momentum]] after the interaction.
===Explosions===
: During an explosion a single [[object]] with zero [[momentum]] splits into two smaller [[object]s.
: The total [[momentum]] before the explosion is zero. Due to '''conservation of momentum''' the total [[momentum]] after the explosion is also zero.
<math>p_{before} = p_{after}</math>
Since:
<math>p = mv</math>
Then:
<math>0 = m_1 v_1 + m_2 v_2</math>
Where:
<math>m_1</math> = The [[mass]] of [[object]] 1.
<math>v_1</math> = The [[velocity]] of [[object]] 1 after the explosion.
<math>m_2</math> = The [[mass]] of [[object]] 2.
<math>v_2</math> = The [[velocity]] of [[object]] 2 after the explosion.
====Example Explosion Calculations====
{| class="wikitable"
| style="height:20px; width:300px; text-align:center;" |An 80kg ice skater and a 90kg ice skater begin at rest and then push away from one another. The 80kg ice skater moves away with a velocity of 0.45m/s. Calculate the [[velocity]] of the 90kg ice skater correct to two [[Significant Figures|significant figures]].
| style="height:20px; width:300px; text-align:center;" |An 18th century cannon of [[mass]] 2000kg fires a 5.5kg cannon ball at a [[velocity]] of 180m/s. Calculate the recoil [[velocity]] of the cannon correct to two [[Significant Figures|significant figures]].
|-
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
p<sub>before</sub> = 0kgm/s
m<sub>1</sub> = 80kg
m<sub>2</sub> = 90kg
v<sub>1</sub> = 0.45m/s
| style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
p<sub>before</sub> = 0kgm/s
m<sub>1</sub> = 2000kg
m<sub>2</sub> = 5.5kg
v<sub>1</sub> = 180m/s
|-
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>p_{before} = p_{after}</math>
<math>0 = m_1 v_1 + m_2 v_2</math>
<math>0 = 80 \times 0.45 + 90 \times v_2</math>
<math>0 = 36 + 90v_2</math>
| style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>p_{before} = p_{after}</math>
<math>0 = m_1 v_1 + m_2 v_2</math>
<math>0 = 2000 \times v_1 + 5.5 \times 180</math>
<math>0 = 2000v_1 + 990</math>
|-
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>90v_2 = -36</math>
<math>v_2 = \frac{-36}{90}</math>
<math>v_2 = -0.40m/s</math>
| style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>2000v_1 = -990</math>
<math>v_1 = \frac{-990}{2000}</math>
<math>v_1 = -0.495m/s</math>
<math>v_1 \approx -0.50m/s</math>
|}
===Elastic Collisions===
===Inelastic Collisions===