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1.30 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the

1.30 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the

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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A 1.30 kg object slides to the right on a surface having a coefficient of kinetic friction 0.250 (Fig. P7.54). The object has a speed of vi = 2.60 m/s when it makes contact with a light spring that has a force constant of 50.0 N/m. The object comes to rest after the spring has been compressed a distance d. The object is then forced toward the left by the spring and continues to move in that direction beyond the spring's unstretched position. The object finally comes to rest a distance D to the left of the unstretched spring.


Figure P7.54
(a) Find the distance of compression d.
                   m
(b) Find the speed v at the unstretched position when the object is moving to the left.
                   m/s
(c) Find the distance D where the object comes to rest.
                    m

 

The image consists of a series of diagrams depicting the motion of a block and a spring system. Here’s a detailed explanation: 1. **Initial State**: - The block with mass \( m \) is moving towards a spring with spring constant \( k \). - The initial velocity of the block is labeled as \( v_i \). - The block is not yet in contact with the spring. 2. **Contact with Spring**: - The block compresses the spring, and its velocity decreases. - The compression of the spring is noted as the block moves past an equilibrium position (dotted line). - The velocity at this point is represented by \( v_f = 0 \), indicating the maximum compression point where the block momentarily stops. 3. **Compression**: - The block continues to compress the spring beyond the equilibrium position, reaching a distance \( d \). 4. **Returning to Equilibrium**: - The spring begins to push the block back in the opposite direction. - The block moves back towards the original position of the spring's equilibrium. 5. **Final State**: - Eventually, the block returns to a point where its velocity equals zero, having moved back a distance \( d \) away from the maximum compression point. This sequence illustrates the conservation of energy, where initial kinetic energy is converted into potential energy in the spring, followed by conversion back into kinetic energy as the spring coiled energy is released, propelling the block back.
Transcribed Image Text:The image consists of a series of diagrams depicting the motion of a block and a spring system. Here’s a detailed explanation: 1. **Initial State**: - The block with mass \( m \) is moving towards a spring with spring constant \( k \). - The initial velocity of the block is labeled as \( v_i \). - The block is not yet in contact with the spring. 2. **Contact with Spring**: - The block compresses the spring, and its velocity decreases. - The compression of the spring is noted as the block moves past an equilibrium position (dotted line). - The velocity at this point is represented by \( v_f = 0 \), indicating the maximum compression point where the block momentarily stops. 3. **Compression**: - The block continues to compress the spring beyond the equilibrium position, reaching a distance \( d \). 4. **Returning to Equilibrium**: - The spring begins to push the block back in the opposite direction. - The block moves back towards the original position of the spring's equilibrium. 5. **Final State**: - Eventually, the block returns to a point where its velocity equals zero, having moved back a distance \( d \) away from the maximum compression point. This sequence illustrates the conservation of energy, where initial kinetic energy is converted into potential energy in the spring, followed by conversion back into kinetic energy as the spring coiled energy is released, propelling the block back.
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