Textbook Question
The double Atwood machine shown in Fig. 4–55 has frictionless, massless pulleys and cords. Determine the tensions FTA and FTC in the cords.
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6. Intro to Forces (Dynamics)
Forces in Connected Systems of Objects
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Three blocks are placed in line on a frictionless table with block B in between blocks A and C. Block A has a mass of , block B has a mass of , and block C has a mass of . A student pushes horizontally on block A with a force of . What is the magnitude of the force of block B on block C?
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Verified step by step guidance1
First, understand that the system of blocks A, B, and C is on a frictionless surface, meaning no external horizontal forces other than the applied force are acting on the system.
Calculate the total mass of the system by adding the masses of blocks A, B, and C: \( m_{\text{total}} = m_A + m_B + m_C = 2.0\,\text{kg} + 4.0\,\text{kg} + 6.0\,\text{kg} \).
Determine the acceleration of the entire system using Newton's second law: \( F = m_{\text{total}} \cdot a \), where \( F \) is the applied force of 24 N. Solve for \( a \) (acceleration).
Once the acceleration is known, focus on block C. The force exerted by block B on block C is the force required to accelerate block C at the same rate as the entire system. Use \( F_{BC} = m_C \cdot a \) to find this force.
Substitute the known values into the equation \( F_{BC} = m_C \cdot a \) to find the magnitude of the force of block B on block C.
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