CP 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. (a) What is the tension in each part of the cord?

Verified step by step guidance

1. Identify the forces acting on each book. The 2.00-kg textbook on the horizontal surface experiences tension in the cord, while the 3.00-kg hanging book experiences both tension and gravitational force.
2. Apply Newton's second law to the 3.00-kg hanging book. The net force is the difference between gravitational force and tension: \( F_{net} = m_2 \cdot g - T_2 \), where \( m_2 = 3.00 \text{ kg} \) and \( g = 9.81 \text{ m/s}^2 \).
3. Apply Newton's second law to the 2.00-kg textbook on the horizontal surface. The net force is the tension in the cord: \( F_{net} = T_1 = m_1 \cdot a \), where \( m_1 = 2.00 \text{ kg} \).
4. Use the kinematic equation to find the acceleration \( a \) of the system: \( s = ut + \frac{1}{2}at^2 \), where \( s = 1.20 \text{ m} \), \( u = 0 \text{ m/s} \), and \( t = 0.800 \text{ s} \). Solve for \( a \).
5. Substitute the value of \( a \) into the equations from steps 2 and 3 to solve for the tensions \( T_1 \) and \( T_2 \) in each part of the cord.

Key Concepts

Newton's Second Law of Motion

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 2.00-kg and 3.00-kg books, which are connected by the cord.

Kinematics

Kinematics involves the study of motion without considering the forces that cause it. Here, it is used to calculate the acceleration of the system by using the given displacement (1.20 m) and time (0.800 s) with the kinematic equation: s = ut + 0.5at^2, where initial velocity (u) is zero since the system starts from rest.

Tension in a Cord

Tension is the force transmitted through a string, rope, or cord when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the cord is affected by the gravitational force on the hanging book and the acceleration of the system. Analyzing the forces on each book separately allows us to find the tension in each part of the cord.