The work done by the applied force on the block against the frictional force is 15.75 J.
Work done is equal to product of force applied and distance moved.
Work = Force x Distance
Given is a 4 kg block is pushed 2m at an acceleration of 0.2 meter per second square up a vertical wall by constant force f applied at an angle of 37 degree with the horizontal if the coefficient of kinetic friction, μ between the block and the wall is 0.30.
From the equilibrium of forces acting on the block, we have
F - f = ma
where, F is applied force, f is frictional force, m is the mass and a is the acceleration.
Frictional force f = μmgsinθ
Substitute the values, we get
Fcos(37) - μmgsin(37) = ma
Fcos(37) - (0.3)(4)(9.8)sin(37) = 4(0.2)
0.799F - 7.077 = 0.8
F = 9.86 N
Work done by the applied force is
W = Fdcosθ
W = 9.86 x 2 x cos(37)
W = 15.75 J
Thus, the work done by the applied force on the block against the frictional force is 15.75 J.
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