Question

Two objects were connected on a rooftop rough incline of 35 degrees via a negligible mass pulley. The 25-kg on the incline experienced a coefficient of kinetic friction of 0.45. The vertical hanging mass was 3.5-x/30kg. Find the acceleration a₁ and string tension.

Answer 1

To solve for the acceleration and string tension of two connected objects on an angled surface with friction, Newton's second law is applied considering all the forces acting on both masses, leading to solving simultaneous equations.

Step-by-step explanation:

The problem involves two objects connected on a rough incline via a negligible mass pulley. To find the acceleration, a₁, and the string tension, we must apply Newton's second law, accounting for the gravitational force components, normal force, frictional force, and tension in the string for both objects.

First, we must determine the masses of both objects. We're given that the mass on the incline is 25 kg and experiences kinetic friction with a coefficient of 0.45. The vertical hanging mass is given by 3.5-x/30 kg. Then we will write down the equations of motion for the objects incorporating the incline angle, friction, and string tension. After setting up the equations, we can solve them simultaneously to find the acceleration of the system and the tension in the string.