A 2.00-kg textbook rests on a frictionless, horizontal surface. A cord attached to the book passes over a pulley whose diameter is 0.150 m, to a hanging book with mass 3.00 kg. The system is released from rest, and the books are observed to move 1.20 m in 0.800 s. What is the tension in each part of the cord?

Verified step by step guidance

1. Start by identifying the forces acting on each book. The 2.00-kg textbook on the frictionless surface experiences tension from the cord, while the 3.00-kg hanging book experiences both tension and gravitational force.
2. Use Newton's second law to set up equations for each book. For the 2.00-kg book, the equation is: \( T_1 = m_1 \cdot a \), where \( T_1 \) is the tension in the cord attached to the 2.00-kg book, \( m_1 = 2.00 \) kg, and \( a \) is the acceleration.
3. For the 3.00-kg hanging book, the equation is: \( m_2 \cdot g - T_2 = m_2 \cdot a \), where \( T_2 \) is the tension in the cord attached to the 3.00-kg book, \( m_2 = 3.00 \) kg, and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).
4. Calculate the acceleration \( a \) using the kinematic equation: \( s = \frac{1}{2} a t^2 \), where \( s = 1.20 \) m is the distance moved, and \( t = 0.800 \) s is the time taken. Rearrange to solve for \( a \).
5. Substitute the calculated acceleration \( a \) into the equations for \( T_1 \) and \( T_2 \) to find the tension in each part of the cord. Ensure to keep the units consistent throughout the calculations.

Key Concepts

Newton's Second Law

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass (F = ma). In this problem, it helps determine the acceleration of the system by considering the forces acting on both the textbook and the hanging book.

Kinematics

Kinematics involves the study of motion without considering the forces that cause it. Using the kinematic equations, we can calculate the acceleration of the books based on their displacement and time. This is crucial for understanding how the system evolves from rest to moving 1.20 m in 0.800 s.

Tension in a Cord

Tension refers to the force transmitted through a string, rope, or cord when it is pulled tight by forces acting at each end. In this scenario, the tension in the cord is affected by the masses of the books and their acceleration. Calculating tension involves analyzing the forces in the system, including gravitational force on the hanging book.