Consider the following four blocks, all of which are attached to identical sprin

Question

Consider the following four blocks, all of which are attached to identical springs: block A: mass = 150·g, spring stretched 10·cm block B: mass = 600·g, spring stretched 20·cm block C: mass = 300·g, spring stretched 20·cm block D: mass = 300·g, spring stretched 20·cm. (a) All the blocks are placed on a level surface that has no significant friction. For each of the following ranking tasks use the symbols > and = to indicate your ranking (ties are possible), listing any that are equal in alphabetical order. For example, if Y and Z are the same and are both greater than X, then you would enter Y=Z>X (note: Z=Y>X would be incorrect, since Y and Z, being equal, must be in alphabetical order). Rank the blocks, from largest to smallest, based on the potential energy stored in the spring attached to each block. largest PE smallest PE (b) The springs are released and the blocks begin to move. Rank the blocks, from largest to smallest, based on their kinetic energy when they reach the mid-point of their oscillation (i.e., when their springs are unstretched)? largest KE smallest KE (c) Compare the relative speed of blocks A and B when they reach their mid-points. Choose one answer only. speed of A > speed of B speed of A = speed of B speed of B > speed of A (d) Compare the relative speed of blocks A and D when they reach their mid-points. Choose one answer only. speed of A > speed of D speed of A = speed of D speed of D > speed of A

Explanation / Answer

given :

block A: mass = 150·g, spring stretched 10·cm

block B: mass = 600·g, spring stretched 20·cm

block C: mass = 300·g, spring stretched 20·cm

block D: mass = 300·g, spring stretched 20·cm

part a)

PE = 1/2 * kx^2

all have the same k (Spring constant ) so PE depends on strech or compress

B = C = D > A

part b )

1/2k(xf^2 - xi^2) = 1/2mv^2

for block A = k(0.05)^2 = 150 * v^2

for block B = k(0.10)^2 = 600 *v^2

for block C = k(0.10)^2 = 300*v^2

for block D = k(0.10)^2 = 300*v^2

B = C = D > A

part c )

for block A = k(0.05)^2 = 150 * va^2

for block B = k(0.10)^2 = 600*vb^2

speed of A = speed of B

part d )

for block A = k(0.05)^2 = 150 * va^2

for block D = k(0.10)^2 = 300*vd^2

vd = sqrt(2)*va

speed of D > speed of A

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