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A box of mass 1.0 kg compresses a spring of constant k = 1000 N/m. The spring and box are placed on a smooth horizontal surface and the spring is compressed by 15 cm. The box is released and spring relaxes causing the box to move away. The box encounters a rough patch of coefficient of friction μk=0.4 extending 2 meters. How fast is the box moving after it clears that patch?
a. 6.2 m/s
b. 4.7 m/s
c. 2.6 m/s
d. 7.4 m/s

Respuesta :

Answer:

option B

Explanation:

given,

mass of the box = 1 Kg

spring constant = k = 1000 N/m

spring is compressed upto = 15 cm = 0.15 m

coefficient of friction = μk =0.4

using conservation of energy

     [tex]\dfrac{1}{2}kx^2 = \dfrac{1}{2}mv^2[/tex]

     [tex]kx^2 =mv^2[/tex]

     [tex]v = \sqrt{\dfra{k}{m}}x[/tex]

     [tex]v = \sqrt{\dfra{1000}{1}}\times 0.15[/tex]

          v = 4.74 m/s

so, the velocity of the box = v = 4.74 m/s

hence, the correct answer is option B

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