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The Proof is Trivial physics edition? Watch

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    (Original post by langlitz)
    I have no idea what M1 is but yeah sorry your solution is correct
    M1 is the first mechanics module in A level maths. This could have been copied out of my textbook

    Explain why a glass prism can separate white light.
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    (Original post by lerjj)
    M1 is the first mechanics module in A level maths. This could have been copied out of my textbook

    Explain why a glass prism can separate white light.
    I wrote this my self in first year for an online thing we had to do where you make questions and everyone answers and rates it. You wouldn't believe how many people got it wrong haha
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    A sphere of mass 3 kg is rolling along a surface (without slipping). It moves with a constant velocity of 2 ms-1 until it reaches a ledge and lands in a fluid where all of its energy is converted into rotational energy and it stays spinning in the fluid. Given the radius of the sphere is 7 cm, calculate the angular velocity of the sphere after it lands in the fluid and which direction the angular velocity vector points (into screen/out of screen)
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    (Original post by langlitz)
    I wrote this my self in first year for an online thing we had to do where you make questions and everyone answers and rates it. You wouldn't believe how many people got it wrong haha
    Looks simple so you don't do it properly...

    Here's a relatively simple one: I connect a buffer resistor and a small piece of silicon in series with a DC battery. Describe and justify how the electrons behave differently in each component.
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    (Original post by langlitz)
    (..)
    Is the height of the drop negligible?
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    (Original post by langlitz)
    A sphere of mass 3 kg is rolling along a surface (without slipping). It moves with a constant velocity of 2 ms-1 until it reaches a ledge and lands in a fluid where all of its energy is converted into rotational energy and it stays spinning in the fluid. Given the radius of the sphere is 7 cm, calculate the angular velocity of the sphere after it lands in the fluid and which direction the angular velocity vector points (into screen/out of screen)
    Is it cheating to look up the kinetic energy of a rotating sphere? Because I do not know it/a sphere's moment of inertia off the top of my head and my calculus isn't too good.

    Not sure about direction. (Don't post a hint though!)
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    When a proton, p, collides at sufficiently high energy with another proton, a proton anti-proton pair can be created in addition to the original protons.

    a). Give the equation for this interaction

    b). How much addition energy is required to create these particles?
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    (Original post by langlitz)
    A sphere of mass 3 kg is rolling along a surface (without slipping). It moves with a constant velocity of 2 ms-1 until it reaches a ledge and lands in a fluid where all of its energy is converted into rotational energy and it stays spinning in the fluid. Given the radius of the sphere is 7 cm, calculate the angular velocity of the sphere after it lands in the fluid and which direction the angular velocity vector points (into screen/out of screen)
    1st attempt

    The ball must experience a force when it enters the fluid to reduce v to 0, which must be pointed to the left. This would be acting on the bottom of the sphere and cause a clockwise angular velocity, which is presumably the way the ball is already rotating. So that the angular velocity vector continues to point into the page.

    The angular velocity will then be given by conservation of energy but I haven't got that far
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    (Original post by lerjj)
    Is it cheating to look up the kinetic energy of a rotating sphere? Because I do not know it/a sphere's moment of inertia off the top of my head and my calculus isn't too good.

    Not sure about direction. (Don't post a hint though!)
    Moment of inertia of a sphere rotating around its centre is 2/5mr^2
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    (Original post by Phichi)
    Is the height of the drop negligible?
    Yeah you can disregard the drop
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    (Original post by lerjj)
    1st attempt

    The ball must experience a force when it enters the fluid to reduce v to 0, which must be pointed to the left. This would be acting on the bottom of the sphere and cause a clockwise angular velocity, which is presumably the way the ball is already rotating. So that the angular velocity vector continues to point into the page.

    The angular velocity will then be given by conservation of energy but I haven't got that far
    I think the idea of the force acting as it hits the surface is a bit ambiguous, there is a lot more considerations to be made. But you could just ignore it for this question, as all the energy is transferred into rotational energy, and we can't make the assumption it'll rotate in the other direction. The direction though is correct.

    Ill let you finish it off lerjj
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    (Original post by Phichi)
    I think the idea of the force acting as it hits the surface is a bit ambiguous, there is a lot more considerations to be made. But you could just ignore it for this question, as all the energy is transferred into rotational energy, and we can't make the assumption it'll rotate in the other direction. The direction though is correct.
    Assume the force is always to the left and is to some function so that it always brings the translational kinetic energy to zero- for all the time that the ball is up to half-submerged, the force causes a clockwise rotation because it acts only on the bottom half. Once the ball is fully submerged, the fluid exerts a force to the left over the entire surface of the sphere and so doesn't cause any rotation. Although this makes some assumptions about the nature of the force, I think this is a reasonable analysis.
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    (Original post by Phichi)
    When a proton, p, collides at sufficiently high energy with another proton, a proton anti-proton pair can be created in addition to the original protons.

    a). Give the equation for this interaction

    b). How much addition energy is required to create these particles?
    a) p + p --> p + p + p + p(bar)
    b) 1876 MeV
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    (Original post by lerjj)
    Assume the force is always to the left and is to some function so that it always brings the translational kinetic energy to zero- for all the time that the ball is up to half-submerged, the force causes a clockwise rotation because it acts only on the bottom half. Once the ball is fully submerged, the fluid exerts a force to the left over the entire surface of the sphere and so doesn't cause any rotation. Although this makes some assumptions about the nature of the force, I think this is a reasonable analysis.
    Ignore the force, it's just a particular problem that the translational K.E becomes zero. In reality the sphere is initially rotating clockwise, so the instantaneous direction of motion of the very bottom of the sphere before it hits the fluid is to the left, the fluid will cause a viscous torque in opposition direction. Can't mention the force really here.
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    (Original post by langlitz)
    Moment of inertia of a sphere rotating around its centre is 2/5mr^2
    then:
     1/2 I \omega ^2 = 1/2 I \omega_0^2 +1/2mv^2

2/5 mr^2 \omega^2=2/5mr^2\omega_0^2+mv^2

    Since the ball travels a distane 2*pi*r for every 2*pi rotation origionally, we can write:
     v=\omega_0 r

2/5 r^2 \omega^2 = 2/5 r^2 \omega_0^2 + \omega_0^2 r^2

\omega ^2=7/2 \omega_0^2 = \dfrac{7v^2}{2r^2}

    After actually substituting values I get: 53 rad/sec? that seems too fast...
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    (Original post by langlitz)
    a) p + p --> p + p + p + p(bar)
    b) 1876 MeV
    Second part is wrong.

    Hint: four momentum
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    (Original post by lerjj)
    then:
     1/2 I \omega ^2 = 1/2 I \omega_0^2 +1/2mv^2

2/5 mr^2 \omega^2=2/5mr^2\omega_0^2+mv^2

    Since the ball travels a distane 2*pi*r for every 2*pi rotation origionally, we can write:
     v=\omega_0 r

2/5 r^2 \omega^2 = 2/5 r^2 \omega_0^2 + \omega_0^2 r^2

\omega ^2=7/2 \omega_0^2 = \dfrac{7v^2}{2r^2}

    After actually substituting values I get: 53 rad/sec? that seems too fast...
    Yep that's what I got If you consider that the final answer doesn't depend the mass, only on the inital velocity and the radius of the ball. Since the ball is travelling at 2 m/s when the radius is only 0.07 m then it spins at 4.55 revs/sec.
    In the fluid it is 53 rad/sec which is 8.43 revs/sec so it isn't that much of an increase really
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    (Original post by lerjj)
    Explain why a glass prism can separate white light.
    The real question is why does light slow down in an optically dense material ?

    Should I make a new thread shortly for this? A formal one? And hope it gets stickied.
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    (Original post by langlitz)
    Yep that's what I got If you consider that the final answer doesn't depend the mass, only on the inital velocity and the radius of the ball. Since the ball is travelling at 2 m/s when the radius is only 0.07 cm then it spins at 4.55 revs/sec.
    In the fluid it is 53 rad/sec which is 8.43 revs/sec so it isn't that much of an increase really
    Okay, I couldn't see what could have gone wrong since the thing making it that high was simply the radius being so small. Good question!
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    (Original post by lerjj)
    Okay, I couldn't see what could have gone wrong since the thing making it that high was simply the radius being so small. Good question!
    Do you plan on doing M4 and M5 at A-Level? If you're interested in moments of interia and such, it's good fun. It's not as hard as made out to be, I personally found relative motion the hardest thing. Was beneficial when I started my degree.
 
 
 
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