Q1. Bank Robbery: Friction & Tension — What is the speed of the safe when it hits the truck 3.0 m below?

Background

Topic: Newton's Laws, Friction, and Kinematics

This problem involves analyzing a system with two masses (a safe and a piece of furniture) connected by a rope over a pulley. The safe falls vertically while the furniture is dragged horizontally, experiencing kinetic friction. The question tests your ability to apply Newton's Second Law, free-body diagrams, friction, and kinematic equations to a coupled system.

Key Terms and Formulas

• Newton's Second Law:

• Kinetic Friction:

• Kinematic Equation (for final speed):

• Weight:

• Normal Force: For horizontal surfaces, (if no vertical forces other than weight and normal)

Step-by-Step Guidance

1. Draw free-body diagrams for both the safe (1000 kg, moving vertically) and the furniture (500 kg, moving horizontally). Label all forces: weight, normal force, tension, and kinetic friction.

2. For the safe: Write Newton's Second Law for vertical motion. The forces are gravity (down) and tension (up): .

3. For the furniture: Write Newton's Second Law for horizontal motion. The forces are tension (right) and kinetic friction (left): .

4. Express the kinetic friction force as and substitute into the equation for the furniture.

5. Combine the two equations to eliminate tension and solve for the acceleration of the system. Set up the equation but do not solve for yet.

6. Once you have the acceleration, use the kinematic equation (with and m) to set up the calculation for the final speed of the safe.

Try solving on your own before revealing the answer!