A light rope is attached to a block with mass 4.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass m is suspended from the other end. When the blocks are released, the tension in the rope is 15.0 N. (d) How does the tension compare to the weight of the hanging block?

Verified step by step guidance

1. First, understand that the tension in the rope is the force that is pulling both blocks. The tension is given as 15.0 N.
2. The weight of the hanging block is the force due to gravity acting on it, which can be calculated using the formula: \( W = m \cdot g \), where \( m \) is the mass of the hanging block and \( g \) is the acceleration due to gravity (approximately 9.81 m/s²).
3. To compare the tension to the weight of the hanging block, we need to express the weight in terms of the tension. Since the tension is the force that accelerates both blocks, it is related to the weight of the hanging block.
4. Consider the forces acting on the hanging block. The tension in the rope acts upward, and the weight of the block acts downward. If the system is in equilibrium or moving with constant velocity, the tension would equal the weight. However, since the blocks are accelerating, the tension is less than the weight.
5. To find the relationship between the tension and the weight, set up the equation for the net force on the hanging block: \( T = m \cdot g - m \cdot a \), where \( a \) is the acceleration of the system. Since \( T = 15.0 \) N, you can solve for \( m \cdot g \) to see how it compares to the tension.

Key Concepts

Newton's Second Law

Newton's Second Law states that the force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). In this scenario, the tension in the rope provides the force that accelerates both blocks, and understanding this law helps determine the relationship between tension and the weight of the hanging block.

Tension in a Rope

Tension is the force transmitted through a rope, string, or cable when it is pulled tight by forces acting at each end. In this problem, the tension in the rope is given as 15.0 N, which is crucial for analyzing the forces acting on both blocks and comparing it to the gravitational force on the hanging block.

Gravitational Force

Gravitational force is the force of attraction between two masses, typically the Earth and an object. It is calculated as the product of the object's mass and the acceleration due to gravity (mg). For the hanging block, this force determines its weight, which must be compared to the tension in the rope to solve the problem.