How would you go about separating the components of a mixture of sand, gravel, salt and iron filings
1 answer:
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a) The initial speed of the clay is 30 m/s
b) The final velocity of the block increases (40 m/s)
Explanation:
a)
We can solve this problem by using the law of conservation of momentum. In fact, in absence of external forces (=no friction), the total momentum of the clay + block system is conserved before and after the collision. Therefore, we can write:
where:
is the mass of the clay
is the initial velocity of the clay
is the mass of the wood block
is the initial velocity of the wood block (at rest)
is the final combined velocity of the clay+block after the collision
Re-arranging the equation, we can find , the speed at which the clay was tossed:
b)
In this second case, the clay is replaced by a bouncy ball, which rebounds back after the collision, instead of sticking with the block.
In this second case, the law of conservation of momentum becomes:
where
is the mass of the ball
is the initial velocity of the ball
is the mass of the wood block
is the initial velocity of the wood block (at rest)
is the velocity of the bouncing ball after the collision (negative because it goes backward)
is the velocity of the block after the collision
Solving for , we find the final velocity of the block:
As we can see, the final velocity of the block has increased. The reason for that is that, as the ball bounces back, part of the total momentum is "carried away" by the ball in the backward direction, and since the total momentum must remain constant, this means that the momentum carried by the block in the forward direction must be larger than the previous situation.
Learn more about conservation of momentum:
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