Answer:
[tex]2.29 \mathrm{m} \text { the block slide if the } \mathrm{u}_{\mathrm{s}}=0.4[/tex]
[tex]4.58 \mathrm{m} \text { the block slide if the } \mathrm{u}_{\mathrm{k}}=0.2[/tex]
Explanation:
Given values
Mass (m) = 2kg
K = 400 N/M
Compressing it 0.3 m
The law of conservation of energy:
[tex]\frac{m v^{2}}{2}+\frac{k x^{2}}{2}=\text { constant }[/tex]
[tex]\text { Where, } \frac{m v^{2}}{2} \text { is kinetic energy of the block. }[/tex]
[tex]\frac{k \Delta l^{2}}{2}[/tex] Energy of the spring deformation.
M mass of the block
x spring deformation
Therefore, if block left the spring (x = 0)
[tex]\frac{m v^{2}}{2}+0=0+\frac{k \Delta l^{2}}{2}[/tex]
Where, Δl is initial spring deformation
[tex]\frac{m v^{2}}{2}=\frac{k \Delta l^{2}}{2}[/tex]
[tex]\mathrm{v}^{2}=\frac{k \Delta l^{2}}{m}[/tex]
[tex]\mathrm{v}=\sqrt{\frac{k}{m} \times \Delta l^{2}}[/tex]
[tex]v=\sqrt{\frac{400}{2} \times(0.3)^{2}}[/tex]
[tex]\mathrm{v}=\sqrt{200 \times 0.09}[/tex]
The law of conservation of energy:
[tex]\frac{m v^{2}}{2}+m g h=\text { constant }[/tex]
Where h is height
[tex]\frac{m v^{2}}{2}+0=0+m g h[/tex]
[tex]\frac{m v^{2}}{2}=m g h[/tex]
Cancel mass "m" each side
[tex]\mathrm{h}=\frac{v^{2}}{2 g}[/tex]
Distance along incline equals
[tex]\begin{array}{ll}{\text { For friction us }} & {\left(L=\frac{h}{u_{s}}\right)} \\ {\text { For friction } u_{k}} & {\left(L=\frac{h}{u_{k}}\right)}\end{array}[/tex]
[tex]\begin{array}{l}{\mathrm{u}_{\mathrm{s}}=0.4} \\ {\mathrm{U}_{\mathrm{k}}=0.2} \\ {\text { For friction } \mathrm{u}_{\mathrm{s}}}\end{array}[/tex]
[tex]\begin{array}{l}{\mathrm{h}=\frac{v^{2}}{2 g u_{s}}} \\ {\mathrm{L}=\frac{4.24^{2}}{2 \times 9.8 \times 0.4}} \\ {\mathrm{L}=\frac{17.9776}{784}}\end{array}[/tex]
[tex]\begin{array}{l}{L=2.29 \mathrm{m}} \\ {2.29 \mathrm{m} \text { the block slide if the } \mathrm{u}_{5}=0.4} \\ {\text { For friction } \mathrm{u}_{\mathrm{k}}} \\ {\mathrm{L}=\frac{4.24^{2}}{2 \times 9.8 \times 0.2}}\end{array}[/tex]
[tex]\begin{array}{l}{L=\frac{17.9776}{3.92}} \\ {L=4.58 \mathrm{m}} \\ {4.58 \mathrm{m} \text { the block slide if the } \mathrm{u}_{5}=0.4}\end{array}[/tex]
