Question

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

Answer 1

option B

Step-by-step 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

`(1)/(2)kx^2 = (1)/(2)mv^2`

`kx^2 =mv^2`

`v = \sqrt{\dfra{k}{m}}x`

`v = \sqrt{\dfra{1000}{1}}* 0.15`

v = 4.74 m/s

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

hence, the correct answer is option B