The masses of blocks A and B in the figure (Figure 1) are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on the floor and are connected by a massless string passing over a massless and frictionless pulley. An upward force \( \vec{F} \) is applied to the pulley.

Find the acceleration \( \vec{a}_A \) of block A when \( F \) is 124 N.

Question

27-02-2025
Physics

High School

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The masses of blocks A and B in the figure (Figure 1) are 20.0 kg and 10.0 kg, respectively. The blocks are initially at rest on the floor and are connected by a massless string passing over a massless and frictionless pulley. An upward force \( \vec{F} \) is applied to the pulley.

Find the acceleration \( \vec{a}_A \) of block A when \( F \) is 124 N.

Answer :

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Final answer:

To find the acceleration of block A in a two-block system connected by a massless string over a frictionless pulley with an applied force, we use Newton's second law by balancing the applied force with the gravitational force on block B and the total mass of the system.

Explanation:

The student's question involves finding the acceleration of block A when an upward force of 124 N is applied to a pulley in a system with two masses, 20.0 kg and 10.0 kg, connected by a massless string over a massless and frictionless pulley.

To find the acceleration of block A, we apply Newton's second law, F = ma, to the system considering both blocks. The force due to gravity on block B is Fg = m * g (where g is the acceleration due to gravity) and acts downward. The tension in the string will act upward on block B and downward on block A. Since the string is massless and the pulley is frictionless, the tension throughout the string is the same. The net force on the system is the applied force F minus the force due to gravity on block B (m2 * g), which equals the total mass times the acceleration ((m1 + m2) * a).

The term Newton's second law helps to show the relationship involved in calculating the acceleration of the blocks. To solve the problem, we set up the equation F - m2 * g = (m1 + m2) * a, plug in the given values, and solve for a, the acceleration of block A.