a 25 kg block is resting on a horizontal surface with coefficient of kinetic fri

Question

a 25 kg block is resting on a horizontal surface with coefficient of kinetic friction 0.5 and static friction 0.8. A spring with spring constant 200 N/m is pressed horizontally against the block on the right side, compressing it. A- how much does the spring compress before the block begins to move. B- what is the acceleration of the block just as it begins to move? a 25 kg block is resting on a horizontal surface with coefficient of kinetic friction 0.5 and static friction 0.8. A spring with spring constant 200 N/m is pressed horizontally against the block on the right side, compressing it. A- how much does the spring compress before the block begins to move. B- what is the acceleration of the block just as it begins to move? a 25 kg block is resting on a horizontal surface with coefficient of kinetic friction 0.5 and static friction 0.8. A spring with spring constant 200 N/m is pressed horizontally against the block on the right side, compressing it. A- how much does the spring compress before the block begins to move. B- what is the acceleration of the block just as it begins to move?

Explanation / Answer

Static Friction, us = 0.8
Kinetic Friction, uk = 0.8
(A)

Friction Force of Block at Rest Position, F = us*N
F = 0.8*m*g
F = 0.8*25*9.8 N
F = 196 N

Let the Compression in spring = x m

Spring Force, Fx = K*x
Fx = 200*x N

Now For Block to Start Moving -

Friction Force = Spring Force

196 = 200*x
x = 0.98 m

Spring compress before the block begins to move, x = 0.98 m

(B)

Now As it Starts moving, Friction Changes From Static to Kinetic Friction.

New Friction Force = uk*N
F = 0.5*25*9.8 N
F = 122.5 N

Now, Let Acceleration of the block = a

Spring Force - Friction Force = m*a
196 - 122.5 = 25*a
Solving for a
a = 2.94 m/s^2

Accleration of the block , a = 2.94 m/s^2

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