Final answer:
To calculate the tension in the rope, we need to consider the weight of the crate, the force of tension, and the force of kinetic friction. By resolving the weight force into its components and using the coefficient of kinetic friction, we can determine the tension in the rope. The tension in the rope is 168.6 N.
Step-by-step explanation:
The weight of the crate is acting downward with a force of 375 N. The force of tension in the rope is acting upward at an angle of 33° above the horizontal. The force of kinetic friction is acting downward and opposing the motion. We can start by resolving the weight force into its components. The component parallel to the ramp is mg × sin(θ), where m is the mass of the crate and g is the acceleration due to gravity. So, the force parallel to the ramp is 15 kg × 9.8 m/s² × sin(33°) = 74.85 N. The force of kinetic friction can be calculated by multiplying the coefficient of kinetic friction (μk) by the normal force, which is equal to the weight of the crate. So, the force of kinetic friction is μk × mg = 0.25 × 375 N = 93.75 N. Since the crate is moving at a constant speed, the force of tension in the rope must be equal to the sum of the parallel force and the force of kinetic friction: T = mg × sin(θ) + μk × mg. Substituting the values, the tension in the rope is T = 74.85 N + 93.75 N = 168.6 N.