Question 174: Work, Energy and Power & Circular Motion

Question

A $$2$$ $$kg$$ block slides on a horizontal floor with a speed of $$4m/s.$$ It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is $$15N$$ and spring constant is $$10, 000$$ $$N/m.$$ The spring compresses by

Accepted Answer

Let the block compress the spring by $$x$$ before coming to rest.
Initial kinetic energy of the block $$=$$ (potential energy of compressed spring) $$+$$ work done due to friction.
$${1 \over 2} 	imes 2 	imes {\left( 4 ight)^2} = {1 \over 2} 	imes 10000 	imes {x^2} + 15 	imes x$$
$$10,000{x^2} + 30x - 32 = 0$$
$$ \Rightarrow 5000{x^2} + 15x - 16 = 0$$
$$	herefore$$ $$x = {{ - 15 \pm \sqrt {{{\left( {15} ight)}^2} - 4 	imes \left( {5000} ight)\left( { - 16} ight)} } \over {2 	imes 5000}}$$
$$\,\,\,\,\, = 0.055m = 5.5cm.$$

Answer

$$8.5cm$$

Answer

$$5.5cm$$

Answer

$$2.5cm$$

Answer

$$11.0cm$$

Work, Energy and Power & Circular Motion

A $2 kg block slides on a horizontal floor with a speed of 4m/s. It strikes a uncompressed spring, and compress it till the block is motionless. The kinetic friction force is 15N and spring constant is 10, 000 N/m.$ The spring compresses by

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