A2.50-kg textbook is forced against a horizontal spring of negligible mass and force constant 250 n/m, compressing the spring a distance of 0.250 m. when released, the textbook slides on a horizontal tabletop with coefficient of kinetic friction \mu_kμ k  = 0.30. use the work–energy theorem to find how far the text-book moves from its initial position before coming to rest.

The distance that the textbook moves from its initial position before coming to rest is 1.0629m

According to the  work-energy theorem, the work done on the spring is equal to the work done by friction

Work done by the spring =

Work done by friction =

k is the spring constant = 250 N/m

x is the distance moved by the spring = 0.250m

is the coefficient of friction = 0.30

m is the mass of the textbook = 2.50kg

g is the acceleration due to gravity = 9.8m/s²

L is the distance from its initial position before coming to rest

Using the formula

Substitute the given parameters into the formula as shown;

Hence the distance that the textbook moves from its initial position before coming to rest is 1.0629m

Learn more here: link

L = 1.06 m

Explanation:

As per work energy theorem we know that work done by all forces must be equal to change in kinetic energy

so here we will have

now we know that

initial and final speed of the book is zero so initial and final kinetic energy will be zero

here we know that

k = 250 N/m

x = 0.250 m

m = 2.50 kg

now plug in all data in it

now we have