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|[[File:InelasticCollision.gif|center]]
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| style="height:20px; width: 300px; text-align:center;" |A trolley of [[mass]] 3kg travels at a [[velocity]] of 4m/s before colliding with a trolley of [[mass]] 1kg travelling in the same direction with a [[velocity]] of 2m/s. After the collision the two trolleys stick together. Calculate the [[velocity]] of the new larger trolley after the collision.
| style="height:20px; width: 300px; text-align:center;" |A lorry of [[mass]] 15Mg travels at a [[speed]] of 20m/s towards a car, of [[mass]] 2500kg traveling in the opposite direction at 10m/s. In this collision the two vehicles stick together. Calculate the [[velocity]] of the combined vehicles after the collision correct to two [[Significant Figures|significant figures]].
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|[[File:CofMCalc5.png|center|300px]]
|[[File:CofMCalc6.png|center|300px]]
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| style="height:20px; width: 300px; text-align:left;" |'''1. State the known quantities'''
m<sub>1</sub> = 3kg
v<sub>1</sub> = 4m/s
m<sub>2</sub> = 1kg
v<sub>2</sub> = 2m/s
| style="height:20px; width: 300px; text-align:left;" |'''1. State the known quantities'''
m<sub>1</sub> = 15Mg = 15x10<sup>3</sup>kg
v<sub>1</sub> = 4m/s
m<sub>2</sub> = 2.5x10<sup>3</sup>kgkg
v<sub>2</sub> = -10m/s This is negative because it is travelling in the opposite direction.
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| style="height:20px; width: 300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_3</math>
<math>3 \times 4 + 1 \times 2 = (3+1) \times v_3</math>
<math>12 + 2 = 4v_3</math>
<math>14 = 4v_3</math>
| style="height:20px; width: 300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
<math>m_1 v_1 + m_2 v_2 = (m_1 + m_2) v_3</math>
<math>15 \times 10^3 \times 20 + 2.5 \times 10^3 \times (-10) = ((15 \times 10^3) + (2.5 \times 10^3)) \times v_3</math>
<math>300000 - 25000 = 17500 \times v_3</math>
<math>275000 = 17500v_3</math>
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| style="height:20px; width: 300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>v_3 = \frac{14}{4}</math>
<math>v_3 = 3.5m/s</math>
| style="height:20px; width: 300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
<math>v_3 = \frac{275000}{17500}</math>
<math>v_3 = 15.7142m/s</math>
<math>v_3 \approx 16m/s</math>
|}