Write the date and ngā whāinga ako in your book
+ +--- + +## Impulse -In order to cause a change in momentum, a force must act upon an object for some amount of time. This is called __impulse__. +> In order to cause a change in momentum, a force must act upon an object for some amount of time. This is called __impulse__. \begin{aligned} & F = ma \newline @@ -210,55 +226,72 @@ In order to cause a change in momentum, a force must act upon an object for some & F \Delta t = \Delta p \end{aligned} -__Impulse__ is therefore $F \Delta t$, the product of force and time which causes the change in momentum. - --- -## Question 6 +### Pātai Whitu (Q7): Satellite in Orbit A satellite is in orbit. It weighs $300kg$ and it has a thruster which exerts a force of $1500N$. How long must the satellite fire its thruster for if it wants to increase its speed from $5000ms^{-1}$ to $6000ms^{-1}$? -__Hint:__ Calculate the change in momentum necessary and then use the impulse relationship. +__Hint:__ Calculate $\Delta p$ first using the velocities, then use the inpulse relationships. --- -### Question 6: Answer - -Step 1: Change in momentum +#### Whakatika {.c2} \begin{aligned} - & \Delta p = mv_{f} - mv_{i} \newline - & = m(v_{f} - v_{i}) \newline - & = 300(6000 - 5000) \newline - & = 300000kgms^{-1} + \Delta p &= mv_{f} - mv_{i} \newline + &= m(v_{f} - v_{i}) \newline + &= 300(6000 - 5000) \newline + &= 300000kgms^{-1} \end{aligned} -Step 2: Impulse - \begin{aligned} - & F \Delta t = \Delta p \newline - & 1500 \Delta t = 300000 \newline - & \Delta t = \frac{300000}{1500} \newline - & \Delta t = 200s + F \Delta t &= \Delta p \newline + 1500 \Delta t &= 300000 \newline + \Delta t &= \frac{300000}{1500} \newline + \Delta t &= 200s \end{aligned} --- -# Mahi Tuatahi +### Pātai Waru (Q8): Cricket -Lena is swinging a bucket of water in a circle around her head to demonstrate circular motion. The length of the rope is 0.75m and it takes 0.84s to go around. +A cricket ball of mass $120g$ is bowled at $30ms^{-1}$ towards a batsman. The batsman hits it away at $90\degree$ to its original velocity, with a speed of $40ms^{-1}$. -1. Explain why the bucket is always accelerating. __(A)__ -2. Calculate the acceleration of the bucket. __(M)__ -3. Name the force that causes the bucket to accelerate as it goes around her head. Explain why the forces cause the bucket to accelerate. __(M)__ +1. Draw a diagram illustrating what has occurred +2. Label the diagram will $p_{i}$ and $p_{f}$ +3. Calculate $\Delta p$ using trigonometry +4. Calculate the force exerted by the batsman, if the bat and ball were in contact for $0.1s$ + +--- + +#### Whakatika {.c2} + + + +--- + +### Whakawai/Practise + +- Textbook Momentum and Impulse Q1-5 + + New: pg. 130 + + Old: pg. 123 --- -## Mahi Tuatahi: Answers +## Akoranga 34 Mahi Tuatahi + +Lena is swinging a bucket of water in a circle around her head to demonstrate circular motion. The length of the rope is $0.75m$ and it takes $0.84s$ to go around. 1. Explain why the bucket is always accelerating. __(A)__ +2. Calculate the acceleration of the bucket. __(M)__ +3. Name the force that causes the bucket to accelerate as it goes around her head. Explain why the force causes the bucket to accelerate and follow a circular path. __(M)__ -The bucket is always accelerating because it is always changing direction, which means the velocity is always changing. +--- + +### Whakatika + +1. Explain why the bucket is always accelerating. __(A)__Write the date and ngā whāinga ako in your book
-- Momentum is conserved during collisions between obejcts and in explosions. -- Momentum before the collision is equal to the momentum afterwards. +--- -- Conservation of momentum only occurs when __no external forces are present__. -- For example gravity or friction either do not apply or have been cancelled by reaction forces. +## Conservation of Momentum -- __Conservation of momentum__ is the only way to solve collision problems. +- Momentum is conserved during collisions between objects and in explosions. + + $p_{i} = p_{f}$ +- Conservation of momentum only occurs when __no external forces are present__. + + An external force would change the momentum ($F \Delta t = \Delta p$)! +- For example, gravity or friction either do not apply or have been cancelled by reaction forces. +- __Conservation of momentum__ is the only way to solve collision problems - Energy is not usually conserved and therefore cannot be used. --- +](https://stickmanphysics.com/wp-content/uploads/2019/11/pool-table-mass-1.gif) + +--- + +](https://uken.zendesk.com/hc/article_attachments/360011696452/8_ball_3_illegal_break.gif) + +--- + +](https://stickmanphysics.com/wp-content/uploads/2020/11/Momentum-Before-Equals-Momentum-After.gif) + +--- + +](https://i.imgur.com/X9tuC.gif) + +--- + ## Conservation of Momentum in 1D -The most straightforward problem you will see is conservation of momentum in 1-dimension. We will use subscript 1 and 2 to indicate object 1 and 2. +- The most straightforward problem you will see is conservation of momentum in 1-dimension. We will use subscript $1$ and $2$ to indicate object $1$ and $2$. +- So that we do not get confused about the velocities, we will also use $u$ to indicate initial velocities and $v$ to indicate final velocities. +- This is an equation representing a collision between two objects. \begin{aligned} - & p_{1} = p_{2} \newline - & m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2} \newline + p_{i} &= p_{f} \newline + p_{1i} + p_{2i} &= p_{1f} + p_{2f} \newline + m_{1}u_{1} + m_{2}u_{2} &= m_{1}v_{1} + m_{2}v_{2} \newline \end{aligned} -So that we do not get confused about the velocities, we will also use $u$ to indicate initial velocities and $v$ to indicate final velocities. +--- + +## Collisions: Elastic vs. Inelastic + +- __Q.__ Can we use energy to calculate collisions? +- __A.__ No, because energy is lost due to friction, meaning that __total kinetic energy is not conserved__. +- However, in __elastic collisions__ total kinetic energy is conserved. +- \sum E_{ki} = \sum E_{kf} +- __NB:__ If total kinetic energy is not conserved, the collision is __inelastic.__ Most collisions are inelastic. --- -## Question 7 +### Pātai Iwa (Q9): The Rifle Jordan is out clay pigeon shooting over the weekend and notices that the gun recoils when he fires. His rifle has mass $4kg$ and fires a bullet of mass $20g$ at $400ms^{-1}$. What is the recoil speed of the rifle into his shoulder? -__Hint:__ Think carefully about the inital speed of both the rifle and bullet before firing. +__Hint:__ Think carefully about the initial speed of both the rifle and bullet before firing. + +\begin{aligned} + \text{(K)} \newline + \text{(U)} \newline + \text{(F)} \newline + \text{(S+S)} +\end{aligned} --- -### Question 7: Answer +#### Whakatika -Both the bullet and the rifle are stationary beforehand. Therefore $m_{1}u_{1} + m_{2}u_{2} = 0$. +Both the bullet and the rifle are stationary beforehand. Therefore $u_{1}$ and $u_{2} = 0$. \begin{aligned} - & m_{1}u_{1} + m_{2}u_{2} = m_{1}v_{1} + m_{2}v_{2} \newline - & 0 = m_{1}v_{1} + m_{2}v_{2} && \text{use realisation from above} \newline - & 0 = (4 \times v_{1}) + (0.02 \times 400) && \text{substitute values} \newline - & 0 = 4v_{1} + 8 \newline - & -8 = 4v_{1} \newline - & v_{1} = \frac{-8}{4} \newline - & v_{1} = -2ms^{-1} + p_{i} &= p_{f} \text{ assuming }F_{net} = 0 \newline + m_{1}u_{1} + m_{2}u_{2} &= m_{1}v_{1} + m_{2}v_{2} \newline + m_{1} \times 0 + m_{2} \times 0 &= m_{1}v_{1} + m_{2}v_{2} && u_{1}=u_{2}=0 \newline + 0 &= (4 \times v_{1}) + (0.02 \times 400) \newline + 0 &= 4v_{1} + 8 \newline + -8 &= 4v_{1} \newline + \frac{-8}{4} &= v_{1} = -2ms^{-1} \end{aligned} --- -# Question 8 +### Pātai Tekau (Q10): Trains + +A shunting car with mass $5\times10^{4}kg$ is moving at $3ms^{-1}$ bumps into a stationary car with mass $3\times10^{4}kg$. They _join_ together in the collision. __Calculate their combined speed _after_ the collision.__ Start by drawing a diagram illustrating before and after the collision. + + + +--- + +### Pātai Tekau mā Tahi (Q11) A moving car collides with a stationary van. The car has mass $950kg$ and the van has mass $1700kg$. The car is travelling $8.0ms^{-1}$ before the collision and $2.0ms^{-1}$ after the collision. @@ -345,7 +428,7 @@ A moving car collides with a stationary van. The car has mass $950kg$ and the va --- -# Question 8: Answer +#### Whakatika ## 1. What quantity is conserved during the collision? __(A)__ @@ -353,7 +436,7 @@ _Momentum is conserved_ --- -## 2. Calculate the __size__ and __direction__ of the car's momentum change. __(E)__ +2. Calculate the __size__ and __direction__ of the car's momentum change. __(E)__ \begin{aligned} & \Delta p = p_{f} - p_{i} \newline @@ -365,7 +448,7 @@ _Momentum is conserved_ --- -## 3. Calculate the speed of the van immediately after the collision. __(M)__ +3. Calculate the speed of the van immediately after the collision. __(M)__ _The van is stationary before the collision._ $u_{2}=0$ @@ -381,7 +464,7 @@ _The van is stationary before the collision._ $u_{2}=0$ --- -## 4. If the average force that the van exerts on the car is $3800N$, calculate how long the collision lasts. __(A)__ +4. If the average force that the van exerts on the car is $3800N$, calculate how long the collision lasts. __(A)__ _The van exerts a force on the car that slows it down. Therefore the force is against the direction of motion, and therefore negative._ @@ -394,7 +477,7 @@ _The van exerts a force on the car that slows it down. Therefore the force is ag --- -## 5. The driver has a bag resting on the passenger seat during the collision. Explain why the bag fell to the floor during the collision. __(E)__ +5. The driver has a bag resting on the passenger seat during the collision. Explain why the bag fell to the floor during the collision. __(E)__ During the collision the van exerts a force upon the car to slow it down. This force acts over a duration of 1.5s. For a force to act upon an object it needs to be attached to or part of the object. A seatbelt attaches the driver to the car allowing the force to act upon the driver through the seatbelt to change their momentum. @@ -402,13 +485,13 @@ Because the bag is not attached to the car the force cannot change its momentum, --- -## 6. The front of modern cars are designed to crumple upon impact. Explain why this is beneficial to people in the car. __(E)__ +6. The front of modern cars are designed to crumple upon impact. Explain why this is beneficial to people in the car. __(E)__ Whether or not a car has a crumple zone, the same change in momentum will occur because of the same change in motion. Using the impulse equation $F \Delta t = \Delta p$ we can see that by increase the time taken for the collision to occur, a smaller force is necessary. This smaller force means that less force affects the driver of the car and therefore reduces the risk of injury. --- -# Question 9 +### Pātai Tekau mā Rua (Q12) A Morris Minor car ($m=750kg$) is travelling at $30ms^{-1}$ and collides head on with a Mercedes Benz car ($m=1600kg$) travelling at $20ms^{-1}$ in the opposite direction. The two cars __lock together__ in the crash. @@ -418,7 +501,9 @@ A Morris Minor car ($m=750kg$) is travelling at $30ms^{-1}$ and collides head on --- -# 1. Calculate the total momentum +#### Whakatika + +1. Calculate the total momentum _Because momentum is conserved, we can calculate the total momentum before OR after the collision._ @@ -432,7 +517,7 @@ _Because momentum is conserved, we can calculate the total momentum before OR af --- -# 2. Calculate the velocity on the combined wreckage after the collision +2. Calculate the velocity on the combined wreckage after the collision \begin{aligned} & \sum p_{i} = \sum p_{f} \newline @@ -445,30 +530,13 @@ _Because momentum is conserved, we can calculate the total momentum before OR af --- -# 3. Would the wreckage keep moving at this velocity? Why or why not? +3. Would the wreckage keep moving at this velocity? Why or why not? In the real world, no, because energy will be lost to the surroundings through heat and sound due to friction on the road, air resistance and engine friction. --- -# Collisions: Elastic vs. Inelastic - -__Q.__ Can we use energy to calculate collisions? - -__A.__ No, because energy is lost due to friction, meaning that __total kinetic energy is not conserved__. - -However, in __elastic collisions__ total kinetic energy is conserved. - -\begin{aligned} - & \sum E_{ki} = \sum E_{kf} -\end{aligned} - -__Note__ - If total kinetic energy is not conserved, the collision is __inelastic.__ Most collisions are inelastic. - ---- - -# Practice Time! - -Mahi Kāinga Book: Q22-26 +### Whakawai -Textbook: 11A and 11B (skip Q4 in 11B) \ No newline at end of file +- Mahi Kāinga Book: Q57-58 +- Textbook: Momentum & Impulse Activity \ No newline at end of file diff --git a/content/12phy/as91171/_index.md b/content/12phy/as91171/_index.md index 96570415..dc7d74ea 100644 --- a/content/12phy/as91171/_index.md +++ b/content/12phy/as91171/_index.md @@ -402,35 +402,33 @@ Homework is issued on a weekly basis. It should be completed in the back of your #### Term 1, Week 9 -32. #### - - __Whakaritenga__ - - +32. #### $p=mv$ & $\Delta p$ in 1D - __Te Whāinga Ako__ - 1. + 1. Be able to use the momentum equation ($p=mv$) + 2. Be able to calculate basic change in momentum situations ($\Delta p = p_{f} - p_{i}$) - __Notes__ - - Slides: - - __Task/Ngohe__ - - + - Follow momentum slides -33. #### - - __Whakaritenga__ - - - - __Te Whāinga Ako__ - 1. +33. #### $\Delta p$ in 2D & Impulse + - __Mahi Tuatahi__ + + 2D momentum question + - __Ngā Whāinga Ako__ + 1. Calculate change of momentum ($\Delta p$) in 2D + 2. Understand and use the concept of impulse ($F\Delta t = \Delta p$) - __Notes__ - - Slides: + - Middle section of slides & questions on momentum - __Task/Ngohe__ - - + - Questions in-slides + - Textbook momentum & impulse questions 1-5 -34. #### - - __Whakaritenga__ - - - - __Te Whāinga Ako__ - 1. +34. #### Conservation of Momentum + - __Ngā Whāinga Ako__ + 1. Understand the assumptions behind momentum conservation + 2. Be able to use conservation of momentum to understand collisions/explosions - __Notes__ - - Slides: + - Slides: Follow slides from Akoranga 34 - __Task/Ngohe__ - - + - Questions embedded in the slides 35. #### - __Whakaritenga__