As seen in Fig. 1, a 5.00 kg mass starts from rest at the top of a frictionless incline at heighty0= 3.25 m and slides to the bottom where it is moving at velocityv1. The level surface at thebottom of the incline is not frictionless. The mass slides along the level surface a distancex2andthen strikes a spring, coming to rest after compressing the spring by distancex3= 0.937 m. Thespring constant (stiffness) of the spring is 255 N/m. Use the bottom of the incline as the referenceposition for gravitational potential energy.1. What is the mechanical energy of the system at the beginning before the mass is released?2. What is the mechanical energy of the system when it reaches the bottom of the incline justafter being released?3. What is the mechanical energy of the system when it stops (for an instant) as the springreaches maximum compression?4. How much work did the frictional force do on the mass as it slid to the right between thebottom of the incline and the point where it came to rest?5. The spring expands pushing the mass back to the left. Find the maximum height that themass will reach as it goes back up the incline. The image illustrates a physics problem involving energy, motion, and friction. It consists of a track with a variety of elements:1. **Inclined Plane (Left Side):** - The track starts with a curved, frictionless inclined plane. A block is positioned at the top of this incline with an initial height labeled as \( y_0 \). - As the block descends the incline, it gains velocity due to gravitational acceleration, reaching a velocity \( v_1 \) at the bottom of the incline.2. **Horizontal Surface with Friction:** - After descending the incline, the block slides onto a horizontal surface. This section of the track is subjected to friction characterized by a coefficient \( \mu_k \). - The block travels a distance \( x_2 \) on this frictional surface.3. **Spring Mechanism (Right Side):** - The block continues to move until it compresses a spring. The original position of the spring is marked. - The block compresses the spring by a distance \( x_3 \), and the total distance from the beginning of the frictional surface to the maximum compression point is \( x_f \).This setup can be used to examine concepts such as energy conservation, kinetic energy, potential energy, work done against friction, and the properties of springs (Hooke's Law). The frictional forces involved play a crucial role in determining how much the spring is compressed and the overall motion of the block.

Work done by gravitational force will be = mgh Work = 5 x 9.8 x 3 =147 J Using Work energy…

Answered: As seen in Fig. 1, a 5.00 kg mass…

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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As seen in Fig. 1, a 5.00 kg mass starts from rest at the top of a frictionless incline at heighty0= 3.25 m and slides to the bottom where it is moving at velocityv1. The level surface at thebottom of the incline is not frictionless. The mass slides along the level surface a distancex2andthen strikes a spring, coming to rest after compressing the spring by distancex3= 0.937 m. Thespring constant (stiffness) of the spring is 255 N/m. Use the bottom of the incline as the referenceposition for gravitational potential energy.

1. What is the mechanical energy of the system at the beginning before the mass is released?

2. What is the mechanical energy of the system when it reaches the bottom of the incline justafter being released?

3. What is the mechanical energy of the system when it stops (for an instant) as the springreaches maximum compression?

4. How much work did the frictional force do on the mass as it slid to the right between thebottom of the incline and the point where it came to rest?

5. The spring expands pushing the mass back to the left. Find the maximum height that themass will reach as it goes back up the incline.