Difference between revisions of "Momentum"

Revision as of 09:16, 15 February 2019

Key Stage 4 Higher

Meaning

Momentum is a vector quantity and the product of mass and velocity of an object.

About Momentum

Momentum is a vector so it has magnitude and direction.

The SI Units of momentum are kilogram metres per second (kgm/s).

Momentum is conserved which means the total momentum before an interaction is the same as the total momentum after the interaction, see Conservation of Momentum.

Forces cause a change in momentum. The quicker the change in momentum the greater the force applied to an object.

Equation

Momentum = Mass x Velocity

\(p = mv\)

Where

\(p\) = Momentum of the object.

\(m\) = Inertial Mass of the object.

\(v\) = Velocity of the object.

Example Calculations

Finding Momentum from Mass and Velocity

A 21g bullet travels at a velocity of 600m/s. Calculate the momentum of the bullet correct to two significant figures.	A 7.6 tonne lorry travels at a velocity of 30m/s. Calculate the momentum of the bullet correct to two significant figures.
1. State the known quantities m = 21g = 0.021kg v = 610m/s	1. State the known quantities m = 7.6 tonnes = 7600kg v = 32m/s
2. Substitute the numbers into the equation and solve. \(p = mv\) \(p = 0.021 \times 610\) \(p = 12.81kgm/s\) \(p \approx 13kgm/s\)	2. Substitute the numbers into the equation and solve. \(p = mv\) \(p = 7600 \times 32\) \(p = 243200kgm/s\) \(p \approx 240000kgm/s\)

Finding Velocity from Mass and Momentum

A 700kg car has a momentum of 2.4x10⁴kgm/s. Calculate the velocity of the car correct to two significant figures.	An asteroid with a mass of 77Mg has a momentum of 3.2x10⁹kgm/s. Calculate the velocity of the asteroid correct to two significant figures.
1. State the known quantities m = 700kg p = 2.4x10⁴kgm/s	1. State the known quantities m = 77Mg = 77x10⁶ p = 3.2x10⁹kgm/s
2. Substitute the numbers and evaluate. \(p = mv\) \(2.4 \times 10^4 = 700v\)	2. Substitute the numbers and evaluate. \(p = mv\) \(3.2 \times 10^9 = (77 \times 10^6 )v\)
3. Rearrange the equation and solve. \(v = \frac{2.4 \times 10^4}{700}\) \(v = 34.285714m/s\) \(v \approx 34m/s\)	3. Rearrange the equation and solve. \(v = \frac{3.2 \times 10^9}{77 \times 10^6}\) \(v = 41.558441m/s\) \(v \approx 42m/s\)

Finding Mass from Velocity and Momentum

A skydiver has a velocity of 53m/s and a momentum of 4400kgm/s. Calculate the mass of the skydiver correct to two significant figures.	A plane travelling with a velocity of 122m/s has a momentum of 9.2x10⁴kgm/s. Calculate the mass of the [plane]] correct to two significant figures.
1. State the known quantities v = 53m/s p = 4400kgm/s	1. State the known quantities v = 122m/s p = 9.2x10⁴kgm/s
2. Substitute the numbers and evaluate. \(p = mv\) \(4400 = 53m\)	2. Substitute the numbers and evaluate. \(p = mv\) \(9.2 \times 10^4 = 122m\)
3. Rearrange the equation and solve. \(m = \frac{4400}{53}\) \(m = 83.01887kg\) \(m \approx 83kg\)	3. Rearrange the equation and solve. \(m = \frac{9.2 \times 10^4}{122}\) \(m = 754.0984kg\) \(m \approx 750kg\)

@@ Line 62: / Line 62: @@
 ====Finding Velocity from Mass and Momentum====
 {| class="wikitable"
-| style="height:20px; width:300px; text-align:center;" |A 700kg car has a [[momentum]] of 2.4x10<sup>4</sup>. Calculate the [[velocity]] of the car
+| style="height:20px; width:300px; text-align:center;" |A 700kg car has a [[momentum]] of 2.4x10<sup>4</sup>kgm/s. Calculate the [[velocity]] of the car correct to two [[Significant Figures|significant figures]].
-| style="height:20px; width:300px; text-align:center;" |Question
+| style="height:20px; width:300px; text-align:center;" |An [[asteroid]] with a [[mass]] of 77Mg has a [[momentum]] of 3.2x10<sup>9</sup>kgm/s. Calculate the [[velocity]] of the [[asteroid]] correct to two [[Significant Figures|significant figures]].
 |-
 | style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
+m = 700kg
+p = 2.4x10<sup>4</sup>kgm/s
 | style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
+m = 77Mg = 77x10<sup>6</sup>
+p = 3.2x10<sup>9</sup>kgm/s
 |-
 | style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
+<math>p = mv</math>
+<math>2.4 \times 10^4 = 700v</math>
 | style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
+<math>p = mv</math>
+<math>3.2 \times 10^9 = (77 \times 10^6 )v</math>
 |-
 | style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
+<math>v = \frac{2.4 \times 10^4}{700}</math>
+<math>v = 34.285714m/s</math>
+<math>v \approx 34m/s</math>
 | style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
+<math>v = \frac{3.2 \times 10^9}{77 \times 10^6}</math>
+<math>v = 41.558441m/s</math>
+<math>v \approx 42m/s</math>
 |}
 ====Finding Mass from Velocity and Momentum====
 {| class="wikitable"
-| style="height:20px; width:300px; text-align:center;" |Question
+| style="height:20px; width:300px; text-align:center;" |A skydiver has a [[velocity]] of 53m/s and a [[momentum]] of 4400kgm/s. Calculate the [[mass]] of the skydiver correct to two [[Significant Figures|significant figures]].
-| style="height:20px; width:300px; text-align:center;" |Question
+| style="height:20px; width:300px; text-align:center;" |A plane travelling with a [[velocity]] of 122m/s has a [[momentum]] of 9.2x10<sup>4</sup>kgm/s. Calculate the [[mass]] of the [plane]] correct to two [[Significant Figures|significant figures]].
 |-
 | style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
+v = 53m/s
+p = 4400kgm/s
 | style="height:20px; width:300px; text-align:left;" |'''1. State the known quantities'''
+v = 122m/s
+p = 9.2x10<sup>4</sup>kgm/s
 |-
 | style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
+<math>p = mv</math>
+<math>4400 = 53m</math>
 | style="height:20px; width:300px; text-align:left;" |'''2. [[Substitute (Maths)|Substitute]] the numbers and [[Evaluate (Maths)|evaluate]].'''
+<math>p = mv</math>
+<math>9.2 \times 10^4 = 122m</math>
 |-
 | style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
+<math>m = \frac{4400}{53}</math>
+<math>m = 83.01887kg</math>
+<math>m \approx 83kg</math>
 | style="height:20px; width:300px; text-align:left;" |'''3. [[Rearrange (Maths)|Rearrange]] the equation and [[Solve (Maths)|solve]].'''
+<math>m = \frac{9.2 \times 10^4}{122}</math>
+<math>m = 754.0984kg</math>
+<math>m \approx 750kg</math>
 |}