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 = 3OOg, spring stretched 10-cm block B: mass = 1200g, spring stretched 20-cm block C: mass = 600g, spring stretched 20 cm block D: mass = 600-g, spring stretched 20-cm. 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 m 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 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 am unstretched)? largest KE smallest KE Now consider the relative speed of the blocks when they reach their mid points. Which of the following comparisons is correct. Choose all that apply. speed of A > speed of B speed of A = speed of B speed of A speed of D speed of A = speed of D speed of A

Explanation / Answer

1.
PE of A = 1/2 k x^2 = 0.5*k *0.1*0.1 = 0.005 k
PE of B = 1/2 k x^2 = 0.5*k *0.2*.2 = 0.02 k
PE of C = = 1/2 k x^2 = 0.5*k *0.2*.2 = 0.02 k
PE of D = 1/2 k x^2 = 0.5*k *0.2*.2 = 0.02 k

Rank of PE: B=C=D>A

2.
KE = PE
=> 1/2 m v^2 = 1/2 k x^2
=>0.5*0.3*v^2 = 0.005 k
=> v^2 =0.005 k/

for A:
=> 1/2 m v^2 = 1/2 k x^2
=>0.5*0.3*v^2 = 0.005 k
=> v^2 =0.005 k/0.5*0.3 = k/30

for B:
=> 1/2 m v^2 = 1/2 k x^2
=>0.5*1.2*v^2 = 0.02 k
=> v^2 =0.02 k/1.2*0.3 = k/18

for C:
=> 1/2 m v^2 = 1/2 k x^2
=>0.5*0.6*v^2 = 0.02 k
=> v^2 =0.02 k/0.6*0.3 = k/9

for D:
=> 1/2 m v^2 = 1/2 k x^2
=>0.5*0.6*v^2 = 0.02 k
=> v^2 =0.02 k/0.6*0.3 = k/9

KE rank will be same as PE rank i.e. : B=C=D>A

3.
speed rank : D=C> B > A

speed A < speed B
speed A< speed D

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