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Answer :
The work done by the 114N force is 4788 J, the work done by the force of friction is -1626.7 J, and the final speed of the block is 18.6 m/s.
To solve this problem, we are dealing with several physical principles like friction, work, and kinetic energy. Let’s deal with it one by one.
The work done by the 114 N force is calculated as the dot product of the force and the displacement which is W=Fdcosθ. Where θ is the angle between force and displacement
. Here, the force with 114N is acting 31° above the horizontal, the angle with respect to horizontal is 31° and the block is displaced horizontally, therefore, cos31°=1. So, Work=W= Fd= 114N*42m= 4788 J.
To find out the work done by the force of friction, we first find the force exerted by friction. This is obtained from the equation F_friction = µ*F_normal, where µ is the coefficient of kinetic friction and F_normal is the normal force.
Since the block is not lifted against gravity, the normal force is m*g = 16.4 kg * 9.8 m/s² = 160.72 N. Then, F_friction = 0.241 * 160.72 N = 38.73 N. The work done by this force over the displacement is W= F_friction*d= 38.73N*42m = -1626.7 J.
The final speed, we can use the work-energy theorem which states that the work done on an object is equal to the change in its kinetic energy.
If the object initially is at rest, the initial kinetic energy is zero. That means Work = ½ m v², where m and v are the object's mass and final velocity. Solving this equation, we get v = (√(2*Work/m)) = √((2*(4788J+1626.7J))/16.4 kg) = 18.6 m/s.
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