To determine the tension required to keep the crate moving at a constant velocity, we need to consider the forces acting on the crate. In this case, we have the force of tension in the rope and the force of friction opposing the motion.
Let's break down the forces acting on the crate:
Weight (W): The weight of the crate is given as 500N. This force acts vertically downward.
Tension (T): The tension in the rope acts at an angle of 30° above the horizontal. We need to find the magnitude of this force.
Friction (F_friction): The force of friction opposes the motion and acts parallel to the surface. The coefficient of dynamic friction is given as 0.40.
Since the crate is moving at a constant velocity, we know that the net force acting on it is zero. This means that the force of tension must balance out the force of friction.
Let's calculate the force of friction first: F_friction = coefficient of dynamic friction * normal force
The normal force is equal to the weight of the crate: Normal force = Weight = 500N
F_friction = 0.40 * 500N = 200N
Now, we can set up the equation for the vertical component of the tension force: T * sin(30°) = Weight = 500N
T * sin(30°) = 500N T = 500N / sin(30°) T ≈ 1000N
Therefore, the tension required to keep the crate moving at a constant velocity is approximately 1000N.