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Two masses, mAmA = 30.0 kgkg and mBmB = 39.0 kgkg are connected by a rope that hangs over a pulley (as in the figure(Figure 1)). The pulley is a uniform cylinder of radius RR = 0.315 mm and mass 4.0 kgkg . Initially, mAmA is on the ground and mBmB rests 2.5 mmabove the ground. If the system is now released, use conservation of energy to determine the speed of mBmB just before it strikes the ground. Assume the pulley is frictionless. Express your answer using three significant figures and include the appropriate units.

Two masses, mAmA = 30.0 kgkg and mBmB = 39.0 kgkg are connected by a rope that hangs over a pulley (as in the figure(Figure 1)). The pulley is a uniform cylinder of radius RR = 0.315 mm and mass 4.0 kgkg . Initially, mAmA is on the ground and mBmB rests 2.5 mmabove the ground. If the system is now released, use conservation of energy to determine the speed of mBmB just before it strikes the ground. Assume the pulley is frictionless. Express your answer using three significant figures and include the appropriate units.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Two masses, mAmA = 30.0 kgkg and mBmB = 39.0 kgkg are connected by a rope that hangs over a pulley (as in the figure(Figure 1)). The pulley is a uniform cylinder of radius RR = 0.315 mm and mass 4.0 kgkg . Initially, mAmA is on the ground and mBmB rests 2.5 mmabove the ground.

If the system is now released, use conservation of energy to determine the speed of mBmB just before it strikes the ground. Assume the pulley is frictionless.

Express your answer using three significant figures and include the appropriate units.
This image illustrates a classic physics problem involving a pulley system. **Description:** - The diagram features a pulley with a radius \( R \). - Two masses, \( m_A \) and \( m_B \), are connected by a rope passing over the pulley. - Mass \( m_A \) is placed on a horizontal surface. - Mass \( m_B \) is hanging and is positioned 2.5 meters above the ground. **Detailed Explanation:** - **Pulley**: The pulley has a fixed radius \( R \) and allows the rope to pass over it, facilitating the movement of the two masses. - **Mass \( m_A \)**: This mass is resting on a surface, suggesting that it might experience normal force from the surface in addition to gravitational force. There may be friction between \( m_A \) and the surface, depending on the context of the problem. - **Mass \( m_B \)**: This mass is suspended freely in the air and will experience gravitational force pulling it downwards. - **Distance between mass \( m_B \) and the ground**: The hanging mass \( m_B \) is 2.5 meters above the ground, indicating the potential drop distance if the system is set into motion. This type of setup is typically used to study the principles of mechanics, such as Newton's laws of motion, tension in the string, acceleration of the masses, and the forces acting on each object. For instance, in a frictionless scenario, the acceleration \( a \) of the system and the tension \( T \) in the rope can be determined using the given masses and the gravitational constant \( g \). This simple yet effective diagram helps visualize the physical interactions and helps in understanding the dynamics of linked masses in a pulley system.
Transcribed Image Text:This image illustrates a classic physics problem involving a pulley system. **Description:** - The diagram features a pulley with a radius \( R \). - Two masses, \( m_A \) and \( m_B \), are connected by a rope passing over the pulley. - Mass \( m_A \) is placed on a horizontal surface. - Mass \( m_B \) is hanging and is positioned 2.5 meters above the ground. **Detailed Explanation:** - **Pulley**: The pulley has a fixed radius \( R \) and allows the rope to pass over it, facilitating the movement of the two masses. - **Mass \( m_A \)**: This mass is resting on a surface, suggesting that it might experience normal force from the surface in addition to gravitational force. There may be friction between \( m_A \) and the surface, depending on the context of the problem. - **Mass \( m_B \)**: This mass is suspended freely in the air and will experience gravitational force pulling it downwards. - **Distance between mass \( m_B \) and the ground**: The hanging mass \( m_B \) is 2.5 meters above the ground, indicating the potential drop distance if the system is set into motion. This type of setup is typically used to study the principles of mechanics, such as Newton's laws of motion, tension in the string, acceleration of the masses, and the forces acting on each object. For instance, in a frictionless scenario, the acceleration \( a \) of the system and the tension \( T \) in the rope can be determined using the given masses and the gravitational constant \( g \). This simple yet effective diagram helps visualize the physical interactions and helps in understanding the dynamics of linked masses in a pulley system.
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