Calculating Kinetic Energy in a Spring Compression Problem

In summary, the problem involves a spring (k=200 N/m) fixed on an inclined plane at angle θ=40° and a 1/0 kg block projected up the plane from an initial position d=0.60m with an initial kinetic energy of 16 J. The question asks for the kinetic energy of the block when it has compressed the spring by 0.20m and the kinetic energy needed to stop the block when it has compressed the spring by 0.40m. The solution involves calculating the change in kinetic energy and potential energy at different distances of compression, including gravitational potential energy.
  • #1
Nicholson
4
0
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

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 that's not what I get
 
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  • #2
Don't forget gravitational PE.
 

FAQ: Calculating Kinetic Energy in a Spring Compression Problem

What is spring kinetic energy?

Spring kinetic energy is the energy that a spring possesses when it is in motion. It is a type of potential energy that is stored in the spring when it is compressed or stretched, and is released when the spring is allowed to return to its original position.

How is spring kinetic energy calculated?

The formula for calculating spring kinetic energy is 1/2 * k * x^2, where k is the spring constant and x is the distance the spring is compressed or stretched. This formula is derived from the equation for potential energy, U = 1/2 * k * x^2, and since kinetic energy is equal to potential energy, the formula is the same.

What is the relationship between spring constant and spring kinetic energy?

The spring constant is a measure of the stiffness of a spring, and it determines the amount of force required to compress or stretch the spring a certain distance. The higher the spring constant, the more energy the spring will have when in motion. This means that the higher the spring constant, the greater the spring kinetic energy will be.

Can spring kinetic energy be converted into other forms of energy?

Yes, spring kinetic energy can be converted into other forms of energy, such as thermal energy or sound energy. When a spring is released, the kinetic energy is converted into heat due to friction, or into sound waves when the spring vibrates. This is known as energy transformation.

What factors affect the amount of spring kinetic energy?

The amount of spring kinetic energy is affected by the spring constant, the distance the spring is compressed or stretched, and the mass of the object attached to the spring. The greater the spring constant and distance, and the smaller the mass, the more spring kinetic energy there will be.

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