Answer :
Final answer:
To find the block's final speed, calculate the work done by the applied force, the work done against friction, and use the work-energy principle to determine the change in kinetic energy, deriving the final speed.
Explanation:
To determine the final speed of a 15.8 kg block dragged over a rough, horizontal surface by a constant force and displaced 12.3 m, we need to calculate the work done by the applied force and the work done against friction. The work done by the force can be calculated using the formula Work = Force × Distance × cos(θ), where θ is the angle of force application. Additionally, the work done against friction is given by Work = frictional force × displacement. Given the coefficient of kinetic friction, the frictional force can be found. Utilizing the work-energy principle, which states that the net work done on an object is equal to its change in kinetic energy, we can then find the final speed of the block.
First, calculate the component of the applied force that acts along the direction of motion, which affects the block's acceleration and the normal force. Then, utilizing the coefficient of kinetic friction, calculate the frictional force opposing the motion. Subtract the work done against friction from the work done by the applied force to find the net work. Finally, use the net work to calculate the final kinetic energy, and thus, the final speed of the block.
