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I think I understand how to begin the problem but when I compute the answers they don't match the selected answers in the back of the book

A spring (k=200 N/m) is fixed at the top of a frictionless plane inclined at angle θ=40°. A 1/0 kg block is projected up the plane, from an initial position that is distance d=0.60m from the end of the relaxed spring, with an initial kinetic energy of 16 J.

a) What is the kinetic energy of the block at the instant it has compressed the spring 0.20 m?

b) With what kinetic energy must the block be projected up the plane if it is to stop momentarily when it has compressed the spring by 0.40m?

Wf=ΔK+ΔU=Kf-Ki+Uf-Ui

a) Ki is the 16 J of KE from the block, Ui is 1/2Kx^2 from the original compressed distance, Uf is 1/2Kx^2 at the instant the spring is compressed to 0.20m.

(Kf-16J) + [(1/2(200 N/m)(0.6)^2)-(1/2(200 N/m)(0.8)^2)]

Answer should be 7 J but I must be off somehow because thats not what I get

## Homework Statement

A spring (k=200 N/m) is fixed at the top of a frictionless plane inclined at angle θ=40°. A 1/0 kg block is projected up the plane, from an initial position that is distance d=0.60m from the end of the relaxed spring, with an initial kinetic energy of 16 J.

a) What is the kinetic energy of the block at the instant it has compressed the spring 0.20 m?

b) With what kinetic energy must the block be projected up the plane if it is to stop momentarily when it has compressed the spring by 0.40m?

## Homework Equations

Wf=ΔK+ΔU=Kf-Ki+Uf-Ui

## The Attempt at a Solution

a) Ki is the 16 J of KE from the block, Ui is 1/2Kx^2 from the original compressed distance, Uf is 1/2Kx^2 at the instant the spring is compressed to 0.20m.

(Kf-16J) + [(1/2(200 N/m)(0.6)^2)-(1/2(200 N/m)(0.8)^2)]

Answer should be 7 J but I must be off somehow because thats not what I get

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