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    Question about volcanoes and momentum is driving me insane
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    What specifically
    ?
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    (Original post by 1jonam16)
    What specifically
    ?
    Question says " A volcano erupts, spewing out 1,000,000,000 rocks of average mass 1kg in a northerly direction. Assuming these rock fragments all go in the same direction, what recoil does the mountain, which has a mass of 1,000,000,000 tonnes, experience? Velocity of rocks = 200m/s and 1 tonne = 1000 kg
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    (Original post by TylerJM)
    Question says " A volcano erupts, spewing out 1,000,000,000 rocks of average mass 1kg in a northerly direction. Assuming these rock fragments all go in the same direction, what recoil does the mountain, which has a mass of 1,000,000,000 tonnes, experience? Velocity of rocks = 200m/s and 1 tonne = 1000 kg
    calculate the momentum of the body of rocks. The mountain experiences equal momentum in the other direction due to the principle of conservation of momentum. Find velocity this way
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    (Original post by TylerJM)
    Question says " A volcano erupts, spewing out 1,000,000,000 rocks of average mass 1kg in a northerly direction. Assuming these rock fragments all go in the same direction, what recoil does the mountain, which has a mass of 1,000,000,000 tonnes, experience? Velocity of rocks = 200m/s and 1 tonne = 1000 kg
    Using the Principle of Conservation of Linear Momentum, we may say that the momentum before the event (eruption) is equal to the momentum after the event as momentum must be conserved.

    Because there is no momentum before the event:

     0 = m_{rocks}v_{rocks} + m_{volcano}v_{volcano}

    Can you use the numerical values in the question to work from here?
    Spoiler:
    Show
    Hence:

    0 = (10^{9})(200) + (10^{9})(1000)v_{volcano}

    Can you see where this has all come from? And also why the velocity must be negative?
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    Spoiler:
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    Momentum before = 0 (as nothing is moving)
    Mass of rocks = 1,000,000,000 * 1 = 1,000,000,000 kg
    Momentum of rocks = mass * velocity = 1,000,000,000 * 200 = 200,000,000,000 kg m/s

    Momentum is conserved so overall momentum = 0
    Momentum of volcano = overall momentum - momentum of rocks = 0 - 200,000,000,000 = - 200,000,000,000

    Mass of volcano = 1,000,000,000 * 1000 = 1,000,000,000,000 kg
    P = mv
    Velocity = momentum ÷ mass = -200,000,000,000 ÷ 1,000,000,000,000 = -0.2 (?) m/s

    You might want to check the calculations, not sure how accurate I was.
    I suggest you attempt it using JakeThomasLee's answer.

    I have given you a full answer underthe spoiler though.
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    (Original post by JakeThomasLee)
    Using the Principle of Conservation of Linear Momentum, we may say that the momentum before the event (eruption) is equal to the momentum after the event as momentum must be conserved.

    Because there is no momentum before the event:

     0 = m_{rocks}v_{rocks} + m_{volcano}v_{volcano}

    Can you use the numerical values in the question to work from here?
    Spoiler:
    Show
    Hence:

    0 = (10^{9})(200) + (10^{9})(1000)v_{volcano}

    Can you see where this has all come from? And also why the velocity must be negative?
    I've got all that I just don't know what the recoil is, are there certain types?
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    (Original post by Lelanor)
    Momentum before = 0 (as nothing is moving)

    Mass of rocks = 1,000,000,000 * 1 = 1,000,000,000 kg
    Momentum of rocks = mass * velocity = 1,000,000,000 * 200 = 200,000,000,000 kg m/s

    Momentum is conserved so overall momentum = 0
    Momentum of volcano = overall momentum - momentum of rocks = 0 - 200,000,000,000 = - 200,000,000,000

    Mass of volcano = 1,000,000,000 * 1000 = 1,000,000,000,000 kg
    P = mv
    Velocity = momentum ÷ mass = -200,000,000,000 ÷ 1,000,000,000,000 = -0.2 (?) m/s

    You might want to check the calculations, not sure how accurate I was.
    Please don't give direct answers. It's usually frowned upon
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    Okay, let me walk you through it. The equation for momentum is p=mv. I.e. momentum is equal to mass * velocity. The question tells you that there are 10 ^9 rocks (1 billion rocks) with a mass of 1kg each. This means the total mass is 10 ^9 kg. It tells you the velocity of these is 2m/s. So to find momentum multiply these values together and you should get 2 * 10^11 kgm/s (the unit of momentum). This is the momentum of the rocks. Now there is a law called conservation of momentum, so the momentum before collision must equal the momentum after collision. And since the momentum before collision is 2 * 10^11 kgm/s then after it it should be the same. Therefore, substitute this into another equation to calculate velocity for the mountain. Now assume the mountain and rocks are one entity and calculate the combined mass of the rocks (10^9 kg) and the mountain (10^12 kg). This should give you the velocity as being 2*10^11 divided by (10^9 + 10^12), giving you a velocity of 0.2m/s to one s.f. in the +Ve direction.
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    Sorry the velocity should be negative but the rest is correct.
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    Lelanor I think you forgot that the masses need to be added
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    (Original post by Student403)
    Please don't give direct answers. It's usually frowned upon
    I couldn't really find a better way to explain without being very confusing (and I didn't see the earlier reply before posting) but I still wanted to help.
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    (Original post by Lelanor)
    I couldn't really find a better way to explain without being very confusing (and I didn't see the earlier reply before posting) but I still wanted to help.
    Ok Just for future
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    (Original post by Student403)
    Ok Just for future
    Okay, thanks

    (Original post by 1jonam16)
    Lelanor I think you forgot that the masses need to be added
    Which masses?
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    (Original post by Lelanor)
    Okay, thanks


    Which masses?
    The mass of the volcano and the mass of the rocks, seeing as they collide and become one object traveling at velocity.
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    (Original post by 1jonam16)
    The mass of the volcano and the mass of the rocks, seeing as they collide and become one object traveling at velocity.
    Surely they're going in opposite directions as the mountain is recoiling? (Although, imagine a volcano taking off from the surface of the earth and travelling with the rocks when it erupts!)
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    Lelanor Sorry the url is patronising but here we go: http://www.dummies.com/how-to/conten...fter-coll.html
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    (Original post by 1jonam16)
    Lelanor Sorry the url is patronising but here we go: http://www.dummies.com/how-to/conten...fter-coll.html
    Going to quote in the question:
    (Original post by TylerJM)
    Question says " A volcano erupts, spewing out 1,000,000,000 rocks of average mass 1kg in a northerly direction. Assuming these rock fragments all go in the same direction, what recoil does the mountain, which has a mass of 1,000,000,000 tonnes, experience? Velocity of rocks = 200m/s and 1 tonne = 1000 kg
    And I drew a (very bad) sketch lol:
    Name:  2016-01-18 22.41.01.jpg
Views: 65
Size:  125.6 KB
    The rocks are going away from the volcano, and the volcano recoils, i.e. moves in the opposite direction. The momentum started out as 0, before the volcano erupted, so it must be 0 at the end, so there must be a negative momentum to counteract the positive one of the rocks.

    The link you sent was about a different type of situation e.g. a van crashing into a car and moving forwards with it.
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    Oops misread the question. Sincere apologies.
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    I know how you feel. When I was learning about volcanoes during Geography I felt like my head was going to erupt.
 
 
 
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