Finding the maximum compression of the spring

[Sean Harold]

Homework Statement

11. Figure 7 shows a 3 kg box starts to move down an inclined plane with initial speed of 5 ms. It travels along the smooth surface and finally compresses the spring which has the spring constant of 400 Nm. Determine the maximum compression of the spring. [Given gravitational acceleration, g = 9.81 ms ²]

Correction:
Theta is not given and the height of the box from the ground is 0.8m

Relevant Equations

By using the conservation of energy,
The initial of total energy=The final of total energy
∑Eᵢ=∑Eғ
Kᵢ+Uᵢ=Kғ+Uғ
mghᵢ+1/2mvᵢ²=mghғ+1/2kx²
(3)(9.81)(0.8)+1/2(3)(5)²=(3)(9.81)(0)+1/2(400)(x)²
61.044=200x²
61.044/200=x²
x²=0.30522
x=0.5525m
Here is the answer I got for the question.

 

[kuruman]

Where did the correction come from? It is not part of the statement of the problem that you posted. Your solution would be correct if the overall vertical drop of the mass were 0.8 m. However, the answer you got does not match the given answer so something is amiss.

 

[Sean Harold]

Where did the correction come from? It is not part of the statement of the problem that you posted. Your solution would be correct if the overall vertical drop of the mass were 0.8 m. However, the answer you got does not match the given answer so something is amiss.

My lecturer told me that she had forgotten to put the height of the object in the question.

 

[kuruman]

My lecturer told me that she had forgotten to put the height of the object in the question.

In that case, I think you should show your solution to your lecturer and ask her why your numerical answer does not match the given answer. Your method is correct and that's what counts.

 

[Sean Harold]

In that case, I think you should show your solution to your lecturer and ask her why your numerical answer does not match the given answer. Your method is correct and that's what counts.

Alright thanks for the help.