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In the figure, a 3.8 kg block is accelerated from rest by a compressed spring of

ID: 2139500 • Letter: I

Question

In the figure, a 3.8 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction ?k = 0.280. The frictional force stops the block in distance D = 8.0 m. What is the original compression distance of the spring?

In the figure, a 3.8 kg block is accelerated from rest by a compressed spring of spring constant 640 N/m. The block leaves the spring at the spring's relaxed length and then travels over a horizontal floor with a coefficient of kinetic friction ?k = 0.280. The frictional force stops the block in distance D = 8.0 m. What is the original compression distance of the spring?

Explanation / Answer

gain in kinetic energy by the block=work done by the spring force ---(1)

after leaving the spring at relaxed position ,it travels over the horizontal floor

loss in the kinetic energy by the block = work done by the frictional force --(2)

so,from (1) and (2)

work done by the spring force =- work done by the frictional force

let the initial compression in the spring be x m

force equation in the vertical direction,N-mg=0

=>N=mg

=>N=3.8*9.8=37.24 N

frictional force,f=0.280*37.24=10.43 N

=> (0.5)*k(x^2-0^2) = -(10.43*D*cos (180))

=>(0.5)*640 *x^2=10.43*8.0

=>x=0.5106 m

=>x=51.06 cm

therefore, the original compression is 51.06 cm

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