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Physics / Physics with MasteringPhysics 4 / Chapter 8 / Problem 105IP

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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Referring to Example Suppose the block is released from

Chapter 8, Problem 105IP

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QUESTION:

Problem 105IP

Referring to Example Suppose the block is released from rest with the spring compressed 5.00 cm. The mass of the block is 1.70 kg and the force constant of the spring is 955 N/m. (a) What is the speed of the block when the spring expands to a compression of only 2.50 cm? (b) What is the speed of the block after it leaves the spring?

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QUESTION:

Problem 105IP

Referring to Example Suppose the block is released from rest with the spring compressed 5.00 cm. The mass of the block is 1.70 kg and the force constant of the spring is 955 N/m. (a) What is the speed of the block when the spring expands to a compression of only 2.50 cm? (b) What is the speed of the block after it leaves the spring?

ANSWER:

Step 1 of 2:-

a)

Here we have to find the speed of the block, when the spring is compressed up to 2.5 cm only.

The force constant is given as,

$k=955\ N/m$ .

Mass of the block is,

$m=1.70\ kg$ .

The initial compression is,

${x}_{i}=5\ cm=0.05\ m$ .

The final compression is,

${x}_{f}=2.5\ cm=0.025\ m$

The conservation of mechanical energy says that,

$K.{E}_{i}+P.{E}_{i}=K.{E}_{f}+P.{E}_{f}$

$\Rightarrow{}0+\frac{1}{2}k{{x}_{i}}^{2}=\frac{1}{2}m{v}^{2}+\frac{1}{2}k{{x}_{f}}^{2}$

$\Rightarrow{}k{{x}_{i}}^{2}-k{{x}_{f}}^{2}=m{v}^{2}$

$\Rightarrow{}v=\sqrt{\frac{k({{x}_{i}}^{2}-{{x}_{f}}^{2})}{m}}\$ -------------(1)

After putting the respective values in the above equation,

$v=\sqrt{\frac{955\times{}(0.0{5}^{2}-0.02{5}^{2})}{1.7}}\$

$=1.026\ m/s$ .

So, the speed of the block at a compression of 2.5 cm is 1.026 m/s.

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