Displacement of spring of a block going down an incline

In summary, the problem involves an inclined plane with an angle of 20.0° and a mass of 2.71 kg placed at a distance of 0.330 m from a spring with a force constant of 455 N/m. The block is projected downward with a speed of 0.750 m/s and the question is asking for the compression distance of the spring when the block momentarily comes to rest. The equation used is dE=dk+du=0 and after substitution and simplification, the answer is incorrect.
  • #1
joedango
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0

Homework Statement


An inclined plane of angle θ = 20.0° has a spring of force constant k = 455 N/m fastened securely at the bottom so that the spring is parallel to the surface as shown in the figure below. A block of mass m = 2.71 kg is placed on the plane at a distance d = 0.330 m from the spring. From this position, the block is projected downward toward the spring with speed v = 0.750 m/s. By what distance is the spring compressed when the block momentarily comes to rest?

Homework Equations


dE=dk+du=0

Kf-Ki+Dfsp-Disp+Dfg-Dig=0
Ki=1/2mv^2
Dfsp=1/2kx^2
Dig= mg[h + x(sin20.0)]

The Attempt at a Solution


Kf,Disp, and Dfg all Equal zero
so by substitution:

-1/2mv^2+1/2kx^2-mg[h + x(sin20.0)]=0
-(2.71)(.75^2)/2+455/2x^2-(2.71*9.8)[0.33+xsin(20)]=0

which simplifies to
227.5x^2-9.084x-9.52=0

My answer is .226, which is the incorrect answer. What am I doing wrong?

Thanks!
 
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  • #2
I forgot to post the picture. Here it is:
7-p-063.gif
 
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1. What is the displacement of the spring of a block going down an incline?

The displacement of the spring of a block going down an incline refers to the change in position of the spring from its original resting position to its final position after the block has traveled down the incline.

2. How is the displacement of the spring affected by the angle of the incline?

The displacement of the spring is affected by the angle of the incline because it determines the distance the block travels and the force acting on the spring. A steeper incline will result in a greater displacement of the spring.

3. What factors influence the displacement of the spring in this scenario?

The displacement of the spring is influenced by the mass of the block, the angle of the incline, the force of gravity, and the stiffness of the spring. These factors all play a role in determining the amount of energy transferred to the spring during the descent of the block.

4. How is the displacement of the spring related to the potential energy of the block?

The displacement of the spring is directly related to the potential energy of the block. As the block descends the incline, its potential energy decreases and is transferred to the spring, causing it to stretch and change its position.

5. Can the displacement of the spring be calculated using a formula?

Yes, the displacement of the spring can be calculated using the formula: x = (mgh) / k, where x is the displacement of the spring, m is the mass of the block, g is the acceleration due to gravity, h is the height of the incline, and k is the spring constant. This formula takes into account the factors that influence the displacement of the spring.

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