4. Two blocks are connected with the massless, non-stretchable rope, and connect

Question

4. Two blocks are connected with the massless, non-stretchable rope, and connected to the spring that is fixed to the wall as shown. One of the blocks is hanging from the side of the table, while the other lies on the table. Mass of each block m=0.5 kg, spring stiffness k=40 N/m, friction coefficient between the block and the table Mu=0.2. The spring is originally unstretched while the blocks are held at rest. Find maximum velocity vmax of the blocks once the system is released (i.e. the hanging block starts to go down).

Explanation / Answer

here,

mass of blocks , m = 0.5 kg

spring constant , k = 40 N/m

friction coefficient , u = 0.2

let the expansion of spring be x

when the spring is in equilibrium

it will accelrate untill net force is equal to zero on the block

m*g - k*x - u * m * g = 0

0.5 * 9.8 - 40 * x - 0.2 * 0.5 * 9.8 = 0

solving for x

x = 0.098 m

as the total energy of spring remains conserved

let vmax is the velocity of block

0.5 * k * x^2 = 0.5 *2* m * v^2 + u mgx

0.5 * 40 * 0.098^2 = 0.5 * 2 * 0.5 * v^2 + 0.2 * 0.5 * 9.8 * 0.098

v = 0.44 m/s

the maximum velocity vmax of the block is 0.44 m/s

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