Final answer:
If Sam is applying a 200 N force at an angle of 30 degrees above the horizontal to pull a 50-kg box at a constant speed across the floor, the coefficient of friction between the box and the floor is 0.354.
Step-by-step explanation:
If Sam is applying a 200 N force at an angle of 30° above the horizontal, we can find the horizontal and vertical components of this force. The horizontal component can be found using the formula Fx = F•cos(θ), where F is the total force and θ is the angle. In this case, Fx = 200 N • cos(30°) = 200 N • 0.866 = 173.2 N.
Since Sam is pulling the box at a constant speed, the horizontal force must equal the force of friction, which can be calculated using the formula Ffriction = μ•N, where μ is the coefficient of friction and N is the normal force. Since the box is being pulled horizontally, the normal force equals the box's weight, which is equal to its mass multiplied by the acceleration due to gravity. N = 50 kg • 9.8 m/s² = 490 N.
Since the force of friction is the only horizontal force acting on the box, Ffriction = 173.2 N. Therefore, the coefficient of friction can be calculated as μ = Ffriction/N = 173.2 N/490 N = 0.354.