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Question

A block mass $$8kg$$ is released from the top of an inclined smooth surface as shown in figure, If spring constant of spring is $$200{N/m}$$ and block comes to rest after compressing spring by $$1m$$ then find the distance travelled by block before it comes to rest:
1063837_add59339f9fb4993b7c5df9f1e565dc2.png


Solution

Given:
Mass $$=8kg$$
K $$= 2000 {N/m}$$
$$h=(s+1)\sin 30^o$$
$$h=(s+1)\times \cfrac{1}{2}$$
Lost in PE of block $$=$$ Gain in PE of spring
$$\Rightarrow mgh=\cfrac{1}{2} kx^2$$
$$\Rightarrow 8\times 10\times \left(\cfrac{s+1}{2}\right)=\cfrac{1}{2}\times 2000\times 1$$
$$\Rightarrow s=24m$$
Total distance travelled before coming to rest $$=s+1=25m$$
965689_1063837_ans_e8c047a5bd394952840dd8429e85ef29.png

Physics

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