- #1
jrwints
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Hi All,
I have a problem (with 3 separate instances) to which I believe I have the answers, but would like check with those more knowledgeable than myself. They revolve around 3 blocks sinking through water and which falls quicker. I am ignoring friction.
Instance 1:
All blocks are exactly the same shape and size. They have different masses however. Which falls quicker?
Instance 2:
All blocks are of different sizes (short/medium/long), but have the same mass. Which falls quicker?
Instance 3:
All blocks are made of the same material but are different sizes (short/medium/long). Which falls quicker?
My understanding of the answers is based upon Newton's second law, buoyancy and free body force diagrams:
W(obj) - W(wat) = mass of object x acceleration (where Weight of water is equal to its density x volume of object x gravity):
a- ( m(o) - m(w) ) g = m(o) a
b- ( p(o) - p(w) ) vg = p(o) v a (mass = density x volume)
1. Using eqn a: Although m(o) increases, m(w) remains constant, therefore acceleration increases and heavier mass falls quicker
2. Using eqn a: As they have the same mass, m(o) remains constant, but m(w) increases as the size of the object increases. Therefore, the smaller object falls quicker
3. Using eqn b: All densities are equal, but as the volume on both sides of the equation cancel each other out, they fall at the same rate
Is this the correct understanding? I believe it is, but it does do your head in!
I have a problem (with 3 separate instances) to which I believe I have the answers, but would like check with those more knowledgeable than myself. They revolve around 3 blocks sinking through water and which falls quicker. I am ignoring friction.
Instance 1:
All blocks are exactly the same shape and size. They have different masses however. Which falls quicker?
Instance 2:
All blocks are of different sizes (short/medium/long), but have the same mass. Which falls quicker?
Instance 3:
All blocks are made of the same material but are different sizes (short/medium/long). Which falls quicker?
My understanding of the answers is based upon Newton's second law, buoyancy and free body force diagrams:
W(obj) - W(wat) = mass of object x acceleration (where Weight of water is equal to its density x volume of object x gravity):
a- ( m(o) - m(w) ) g = m(o) a
b- ( p(o) - p(w) ) vg = p(o) v a (mass = density x volume)
1. Using eqn a: Although m(o) increases, m(w) remains constant, therefore acceleration increases and heavier mass falls quicker
2. Using eqn a: As they have the same mass, m(o) remains constant, but m(w) increases as the size of the object increases. Therefore, the smaller object falls quicker
3. Using eqn b: All densities are equal, but as the volume on both sides of the equation cancel each other out, they fall at the same rate
Is this the correct understanding? I believe it is, but it does do your head in!