Five different experiments are carried out. In each experiment, a block is attac
ID: 1454998 • Letter: F
Question
Five different experiments are carried out. In each experiment, a block is attached to a horizontal spring. The block is pulled back a certain distance and released. The block oscillates back and forth on a frictionless surface. Rank the amplitude of oscillation for each of the following situations (1-5). Rank the smallest amplitude as 1.
E1 = A block of mass 2M is attached to a spring with a spring constant k, pulled back a distance d, and released.
E2 = A block of mass M is attached to a spring with a spring constant (1/2)k, pulled back a distance d, and released.
E3 = A block of mass M is attached to a spring with a spring constant k, pulled back a distance d, and released.
E4 = A block of mass M is attached to a spring with a spring constant 2k, pulled back a distance d, and released.
E5 = A block of mass M is attached to a spring with a spring constant k, pulled back a distance 2d, and released.
Explanation / Answer
Please Note down following concepts :
1.Spring is horizontal and no other horizontal force is acting , so mean position of SHM will be the position where spring is in natural length.
2.Amplitude of motion will be distance between mean position to extreme one , or Half of distance between two extreme
3. Spring is conservative force hence total energy will be conserved
4 .At extreme postion speed will be zero
Now
Since intially Spring was elongated by a distance S and then left to oscillate so at other extreme position the spring must have same potential energy thus spring will be compressed by S
Elongation S in spring was first extreme
Compression S in spring will be second Extreme
Thus amplitude A= 2S/2 =S
Note : Amplitude will not depend on the spring constant and mass
so A= d for E1, E2,E3, and E4
and A= 2d for E5
Hence
E5 > E4 =E3 =E2= E1
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