Final answer:
To find the force required to move the box at a constant speed, we can use the equation F_friction = μ*N, where μ is the coefficient of friction and N is the normal force on the box. By analyzing the forces acting on the box, we can determine that the force required to move the box at a constant speed is equal to the force of friction. Using trigonometry, we can find the specific force required by calculating the parallel force component of the tension force applied to the rope. So the correct answer is Option C.
Step-by-step explanation:
To find the force required to move the box at a constant speed, we need to calculate the friction force acting on the box. The friction force can be found using the equation F_friction = μ*N, where μ is the coefficient of friction and N is the normal force on the box. Since the box is on a horizontal floor and is not accelerating vertically, the normal force is equal to the weight of the box, which is given by N = m*g, where m is the mass of the box and g is the acceleration due to gravity.
The force required to move the box at a constant speed is equal to the force of friction. In this case, the force of friction is given by F_friction = μ*N = μ*m*g. Since the box is being pulled by a rope at an angle of 20 degrees, the force applied to the rope can be divided into two components: F_parallel and F_perpendicular. The force required to move the box at a constant speed is equal to F_parallel.
Using trigonometry, we can find that F_parallel = F_applied*cosθ, where θ is the angle between the rope and the floor. Therefore, the force required to move the box at a constant speed is F_parallel = F_tension*cosθ. Substituting the known values into the equation, we get F_parallel = T*cosθ = (m*g + μ*m*g)*(cosθ). Plugging in the given values, we have F_parallel = (68 kg * 9.8 m/s^2 + 0.6 * 68 kg * 9.8 m/s^2) * cos(20 degrees) = 636.5 N. Therefore, the correct answer is option C) 636.5 N.