A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg, frictionless pulley, as shown in the figure. A constant 10 N tension is applied to the other end of the rope. (a) Derive a relationship for the acceleration of the block in terms of r, g, I of the pulley, and mass of the block. (b) What is the numerical value of the acceleration? (c) Starting from rest, how long does it take the block to move 30 cm?
A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg, frictionless pulley, as shown in the figure. A constant 10 N tension is applied to the other end of the rope. (a) Derive a relationship for the acceleration of the block in terms of r, g, I of the pulley, and mass of the block. (b) What is the numerical value of the acceleration? (c) Starting from rest, how long does it take the block to move 30 cm?
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
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Transcribed Image Text:**Problem Description:**
A 1.5 kg block is connected by a rope across a 50-cm-diameter, 2.0 kg, frictionless pulley, as shown in the figure. A constant 10 N tension is applied to the other end of the rope.
**Tasks:**
(a) Derive a relationship for the acceleration of the block in terms of \( r \), \( g \), \( I \) of the pulley, and mass of the block.
(b) What is the numerical value of the acceleration?
(c) Starting from rest, how long does it take the block to move 30 cm?
**Diagram Explanation:**
The diagram shows a vertical pulley system with a 1.5 kg block hanging on the left side. A rope runs over the top of a pulley with a diameter of 50 cm, and a constant tension of 10 N is applied to the right side of the rope. The pulley is frictionless and has a mass of 2.0 kg.
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