(A) Given: Mass $m = 0.18 \ kg$,Spring constant $k = 2 \ N/m$,Coefficient of friction $\mu = 0.1$,Displacement $x = 0.06 \ m$,Initial velocity $V = N/

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(A) Given: Mass $m = 0.18 \ kg$,Spring constant $k = 2 \ N/m$,Coefficient of friction $\mu = 0.1$,Displacement $x = 0.06 \ m$,Initial velocity $V = N/10 \ m/s$.Using the Work-Energy Theorem,the work done by all forces equals the change in kinetic energy:$W_{\text{friction}} + W_{\text{spring}} = K_f - K_i$$-(\mu mg)x - \frac{1}{2}kx^2 = 0 - \frac{1}{2}mV^2$Substituting the values:$-(0.1 \times 0.18 \times 10 \times 0.06) - \frac{1}{2} \times 2 \times (0.06)^2 = -\frac{1}{2} \times 0.18 \times V^2$$-(0.0108) - (0.0036) = -0.09 V^2$$-0.0144 = -0.09 V^2$$V^2 = \frac{0.0144}{0.09} = 0.16$$V = \sqrt{0.16} = 0.4 \ m/s$Given $V = N/10$,so $0.4 = N/10 \implies N = 4$.

Class 11 Physics Work, Energy, Power and Collision Mix Examples-Work, Energy, Power and Collision

Medium

$A$ block of mass $0.18 \ kg$ is attached to a spring of force constant $2 \ N/m$. The coefficient of friction between the block and the floor is $0.1$. Initially,the block is at rest and the spring is unstretched. The block is pushed as shown in the figure. The block slides a distance of $0.06 \ m$ and comes to rest. If the initial velocity of the block is $V = N/10 \ m/s$,then what is the value of $N$?

A
$4$
B
$2$
C
$5$
D
$1$

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Mix Examples-Work, Energy, Power and Collision

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