Final answer:
To find the incline angle (θ) of the chute, we can use the concept of friction. The incline angle can be calculated using the equation θ = arctan(V_1 / (V_2 - μ_k * V_1)), where μ_k is the coefficient of friction and V_1 and V_2 are the speeds of conveyor belts A and B respectively.
Step-by-step explanation:
To find the incline angle (θ) of the chute, we can use the concept of friction. When an object is delivered to belt B without slipping, the friction force between the object and the chute helps to maintain its speed.
The friction force is given by the equation:
F_friction = μ_k * N
where μ_k is the coefficient of friction and N is the normal force. The normal force is equal to the weight of the object:
N = m * g
where m is the mass of the object and g is the acceleration due to gravity.
Since the object is delivered at a speed of 0.9 m/s, the friction force must be equal to the force applied by the conveyor belt (F_applied) to keep the object moving without slipping:
F_applied = F_friction
Combining these equations, we have:
μ_k * m * g = F_applied
From the given information, the coefficient of friction (μ_k) is 0.5 and the speed of conveyor belt A (V_1) is 0.3 m/s. Therefore, the incline angle (θ) can be calculated using the equation:
θ = arctan(V_1 / (V_2 - μ_k * V_1))