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Exercise 4.13 Hints: Getting Started | I'm Stucl What if an additional mass is attached to the ball in Example 4.13? How large must the mass be to increase the downward acceleration by 50%? kg

Exercise 4.13 Hints: Getting Started | I'm Stucl What if an additional mass is attached to the ball in Example 4.13? How large must the mass be to increase the downward acceleration by 50%? kg

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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**Example 4.13 Connected Objects** **Goal** Use both the general method and the system approach to solve a connected two-body problem involving gravity and friction. **Problem** A block with mass \( m_1 = 4.00 \, \text{kg} \) and a ball with mass \( m_2 = 7.30 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley, as shown in Figure 4.23a. The coefficient of kinetic friction between the block and the surface is 0.300. (a) Find the acceleration of the two objects and the tension in the string. (b) Check the answer for the acceleration by using the system approach. **Strategy** Connected objects are handled by applying Newton’s second law separately to each object. The free-body diagrams for the block and the ball are shown in Figure 4.23b, with the +x-direction to the right and the +y-direction upwards. The magnitude of the acceleration for both objects has the same value, \( |a_1| = |a_2| = a \). The block with mass \( m_1 \) moves in the positive x-direction, and the ball with mass \( m_2 \) moves in the negative y-direction, so \( a_1 = -a_2 \). Using Newton’s second law, we can develop two equations involving the unknowns \( T \) and \( a \) that can be solved simultaneously. In part (b), treat the two masses as a single object, with the gravity force on the ball increasing the combined object's speed and the friction force on the block retarding it. The tension forces then become internal and don’t appear in the second law. **Figures Explanation:** - **Figure 4.23a**: Illustrates two objects connected by a light string that passes over a frictionless pulley. The setup depicts a block on a flat surface and a ball hanging off the edge. - **Figure 4.23b**: Shows the free-body diagrams for the objects. The block has forces labeled \( \vec{f}_k \) (friction force), \( m_1 \vec{g} \) (gravitational force), and the normal force \( \vec{n} \), with tensions \( \vec{T} \) acting to the right. The ball illustrates
Transcribed Image Text:**Example 4.13 Connected Objects** **Goal** Use both the general method and the system approach to solve a connected two-body problem involving gravity and friction. **Problem** A block with mass \( m_1 = 4.00 \, \text{kg} \) and a ball with mass \( m_2 = 7.30 \, \text{kg} \) are connected by a light string that passes over a frictionless pulley, as shown in Figure 4.23a. The coefficient of kinetic friction between the block and the surface is 0.300. (a) Find the acceleration of the two objects and the tension in the string. (b) Check the answer for the acceleration by using the system approach. **Strategy** Connected objects are handled by applying Newton’s second law separately to each object. The free-body diagrams for the block and the ball are shown in Figure 4.23b, with the +x-direction to the right and the +y-direction upwards. The magnitude of the acceleration for both objects has the same value, \( |a_1| = |a_2| = a \). The block with mass \( m_1 \) moves in the positive x-direction, and the ball with mass \( m_2 \) moves in the negative y-direction, so \( a_1 = -a_2 \). Using Newton’s second law, we can develop two equations involving the unknowns \( T \) and \( a \) that can be solved simultaneously. In part (b), treat the two masses as a single object, with the gravity force on the ball increasing the combined object's speed and the friction force on the block retarding it. The tension forces then become internal and don’t appear in the second law. **Figures Explanation:** - **Figure 4.23a**: Illustrates two objects connected by a light string that passes over a frictionless pulley. The setup depicts a block on a flat surface and a ball hanging off the edge. - **Figure 4.23b**: Shows the free-body diagrams for the objects. The block has forces labeled \( \vec{f}_k \) (friction force), \( m_1 \vec{g} \) (gravitational force), and the normal force \( \vec{n} \), with tensions \( \vec{T} \) acting to the right. The ball illustrates
**Exercise 4.13** What if an additional mass is attached to the ball in Example 4.13? How large must the mass be to increase the downward acceleration by 50%? [Input box] kg Why isn't it possible to add enough mass to double the acceleration? Doubling the acceleration would make it bigger than gravity, which isn't possible.
Transcribed Image Text:**Exercise 4.13** What if an additional mass is attached to the ball in Example 4.13? How large must the mass be to increase the downward acceleration by 50%? [Input box] kg Why isn't it possible to add enough mass to double the acceleration? Doubling the acceleration would make it bigger than gravity, which isn't possible.
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