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Ch 05: Applying Newton's Laws
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook
Chapter 5, Problem 17d

A light rope is attached to a block with mass 4.004.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass mm is suspended from the other end. When the blocks are released, the tension in the rope is 15.015.0 N. How does the tension compare to the weight of the hanging block?

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Step 1: Begin by understanding the forces acting on the system. The tension in the rope (T = 15.0 N) is the same throughout the rope because the pulley is frictionless and massless. The hanging block experiences two forces: its weight (W = m * g) acting downward and the tension (T) acting upward.
Step 2: Recall that the weight of the hanging block is given by the formula: W=mg, where g is the acceleration due to gravity (approximately 9.8 m/s²). This weight is the force pulling the block downward.
Step 3: Compare the tension in the rope (T = 15.0 N) to the weight of the hanging block. If the tension is less than the weight, the block will accelerate downward. If the tension equals the weight, the block will remain stationary. If the tension is greater than the weight, the block will accelerate upward.
Step 4: To determine how the tension compares to the weight, calculate the weight of the hanging block using the formula W=mg. Substitute the value of m (mass of the hanging block) and g into the equation.
Step 5: Once the weight is calculated, compare it to the given tension (15.0 N). This comparison will reveal whether the tension is greater than, less than, or equal to the weight of the hanging block.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Tension in a Rope

Tension is the force transmitted through a rope or string when it is pulled tight by forces acting from opposite ends. In this scenario, the tension in the rope is crucial for understanding the forces acting on both the block on the surface and the hanging block. It is the same throughout the rope in a frictionless system, meaning the tension experienced by the hanging block is equal to that experienced by the block on the surface.
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Weight of an Object

The weight of an object is the force exerted on it due to gravity, calculated as the product of its mass and the acceleration due to gravity (W = mg). For the hanging block, its weight determines how much force is acting downward, which is essential for comparing it to the tension in the rope. In this case, the weight of the hanging block will influence whether it accelerates downward or remains at rest.
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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). This principle helps analyze the forces acting on both blocks in the system. By applying this law, one can determine how the tension in the rope relates to the weight of the hanging block and the resulting motion of the system.
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Related Practice
Textbook Question

A light rope is attached to a block with mass 4.004.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass mm is suspended from the other end. When the blocks are released, the tension in the rope is 15.015.0 N. What is the acceleration of either block?

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Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about 6060 cm. During the jump, the person's body from the knees up typically rises a distance of around 5050 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. In terms of this jumper's weight w, what force does the ground exert on him or her during the jump?

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Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about 6060 cm. During the jump, the person's body from the knees up typically rises a distance of around 5050 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. Draw a free-body diagram of the person during the jump.

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Textbook Question

A light rope is attached to a block with mass 4.004.00 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 15.015.0 N. Find mm.

2
views
Textbook Question

When jumping straight up from a crouched position, an average person can reach a maximum height of about 6060 cm. During the jump, the person's body from the knees up typically rises a distance of around 5050 cm. To keep the calculations simple and yet get a reasonable result, assume that the entire body rises this much during the jump. With what initial speed does the person leave the ground to reach a height of 6060 cm?

3
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Textbook Question

A light rope is attached to a block with mass 4.004.00 kg that rests on a frictionless, horizontal surface. The horizontal rope passes over a frictionless, massless pulley, and a block with mass mm is suspended from the other end. When the blocks are released, the tension in the rope is 15.015.0 N. Draw two free-body diagrams: one for each block.

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