Q1. Two bodies P and Q on a smooth horizontal surface are connected by a light cord. The mass of P is greater than that of Q. A horizontal force F is applied to Q, accelerating the bodies to the right. What is the magnitude of the force exerted by the connecting cord on body P?

Background

Topic: Newton's Laws of Motion, Tension in Cords

This question tests your understanding of how forces are transmitted through a cord connecting two masses, and how Newton's second and third laws apply to systems of connected objects.

Key Terms and Formulas:

• Tension (): The force transmitted through the cord.

• Newton's Second Law:

• System acceleration: Both blocks accelerate together, so

• Force on P: The tension in the cord is what accelerates P.

Step-by-Step Guidance

1. Identify the total mass of the system: .

2. Apply Newton's second law to the entire system: .

3. Determine the acceleration: .

4. Apply Newton's second law to block P: The only horizontal force on P is the tension , so .

Try solving on your own before revealing the answer!

Q2. Two objects are connected by a very light flexible string as shown in the figure, where M = 1.60 kg and m = 1.00 kg. Ignore friction and the mass of the pulley.

Background

Topic: Atwood's Machine, Newton's Second Law

This question tests your ability to analyze a classic Atwood's machine setup, where two masses are connected by a string over a pulley, and you must determine acceleration and tension.

Key Terms and Formulas:

• Newton's Second Law:

• Tension (): The force in the string.

• Acceleration:

Step-by-Step Guidance

1. Draw free-body diagrams for each mass (M and m).

2. Write Newton's second law for each mass: (downward): ; (upward): .

3. Add the two equations to eliminate and solve for .

4. Once you have , substitute back to solve for .

Try solving on your own before revealing the answer!

Q3. A wooden block A of mass 7.0 kg slides on a frictionless table when pulled using a massless string and pulley array by a hanging box B of mass 9.0 kg, as shown in the figure. What is the acceleration of block A as it slides on the frictionless table?

Background

Topic: Pulley Systems, Newton's Second Law, Constraint Relations

This question tests your understanding of how to analyze a system with a frictionless table and a pulley, and how the acceleration of one block relates to the other.

Key Terms and Formulas:

• Newton's Second Law:

• Constraint: The acceleration of block A is related to block B by the pulley setup.

• For frictionless systems:

Step-by-Step Guidance

1. Draw free-body diagrams for both blocks.

2. Write Newton's second law for block A (horizontal) and block B (vertical).

3. Set up the equations: for block A, for block B.

4. Add the equations to eliminate and solve for .

Try solving on your own before revealing the answer!