To determine the tension required to keep the crate moving at a constant velocity, we need to consider the forces acting on the crate. The main forces involved are the gravitational force and the force of friction.
Gravitational force (weight): The weight of the crate is given as 500N, which is the force exerted vertically downward. We can decompose this force into its horizontal and vertical components. The vertical component is given by: Vertical component = Weight * sin(θ) = 500N * sin(30°) = 250N
Force of friction: The force of friction can be calculated using the coefficient of dynamic friction and the normal force. The normal force is the perpendicular force exerted by the surface on the crate, which is equal to the vertical component of the weight. Therefore, the normal force is 250N.
Force of friction = coefficient of dynamic friction * normal force = 0.40 * 250N = 100N
- Tension: The tension in the rope must balance the force of friction to keep the crate moving at a constant velocity. Since the crate is moving at a constant velocity, the net force acting on it must be zero. The horizontal component of the weight and the tension force must cancel out the force of friction.
Horizontal component of weight = Weight * cos(θ) = 500N * cos(30°) = 433.01N
Net force = Tension - Force of friction = 433.01N - 100N = 333.01N
Since the net force is zero, the tension force required to keep the crate moving at a constant velocity is 333.01N.