Q1. What must be the mass of the hanging block if it is to descend 12.0 m in the first 3.00 s after the system is released from rest? (Given: kg, , )

Background

Topic: Newton's Laws of Motion, Friction, and Kinematics

This question tests your ability to analyze a system of two connected masses, one on an inclined plane with friction and one hanging vertically, using Newton's second law and kinematic equations.

Key Terms and Formulas

• Newton's Second Law:

• Kinetic Friction:

• Kinematic Equation for distance: (for motion starting from rest)

• Normal Force on Incline:

• Force components along incline: (down the incline)

Step-by-Step Guidance

1. Start by identifying the forces acting on each block. For (on the incline): gravity (split into parallel and perpendicular components), friction, and tension. For (hanging): gravity and tension.

2. Write Newton's second law for each block. For : . For : .

3. Find the normal force for : .

4. Use the kinematic equation to find the acceleration needed for to descend 12.0 m in 3.00 s: .

5. Substitute the value of into the equations for tension and solve for using the equation for .

Try solving on your own before revealing the answer!