A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pu

Question

A very light ideal spring with a spring constant (force constant) of 2.5 N/cm pulls horizontally on an 18-kg box that is resting on a horizontal floor. The coefficient of static friction between the box and the floor is 0.65, and the coefficient of kinetic friction is 0.45.

(a) How long is the spring just as the box is ready to move?
(b) If the spring pulls the box along with a constant forward velocity of 1.75 m/s, how long is the spring?

(c) How long is the spring if it pulls the box forward at a constant 2.75 m/s?

The answers are 46cm, 32 cm, and 32 cm

If you could provide how to do each part, that would be wonderful! Thank you!

Explanation / Answer

spring constant (force constant) of 2.5 N/cm

pulls horizontally on an 18-kg

coefficient of static friction between the box and the floor is 0.65,

coefficient of kinetic friction is 0.45.

m*g

18(9.81) = 176.58 N

Max static friction force = (176.58)(0.65) 115 N

Spring deformation length = 115/2.5 = 46 cm the answer to question part (a)

Kinetic friction force = (176.58)(0.45) 79.5 N

(b) & (c) Spring deformation length = 79.5/2.5 = 31.8 = 32 cm both answers are identical but this length is not the answer/s asked for,

Note: This question can not be answered because the original length of the ideal light spring is not given. The only thing that CAN be determined is the deformation length, in each case, for this spring.

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