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a) Determine the potential energy within the spring when the slider is at point A and determine the potential energy in the spring when the slider is at point B? b) Calculate the speed velocity b of the slider when it reaches point B. c) Assume now that the normal force exerted by the guide on the slider at point B is 84.1 N, find the radius of curvature ρB of the guide.

a) Determine the potential energy within the spring when the slider is at point A and determine the potential energy in the spring when the slider is at point B? b) Calculate the speed velocity b of the slider when it reaches point B. c) Assume now that the normal force exerted by the guide on the slider at point B is 84.1 N, find the radius of curvature ρB of the guide.

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A slider with a mass of 0.6 kg is connected to a spring with a of stiffness k = 120 N/m and, as pictured below, slides down a smooth parabolic guide. This guide lies in a vertical plane and the slider is released from a stationary position. The length of the spring when unstretched is 0.2 m.

a) Determine the potential energy within the spring when the slider is at point A and determine the potential energy in the spring when the slider is at point B?

b) Calculate the speed velocity b of the slider when it reaches point B.

c) Assume now that the normal force exerted by the guide on the slider at point B is 84.1 N, find the radius of curvature ρB of the guide.

d) Determine the initial speed velocity a (at point A) (downward direction) that the slider would need to reach a speed at B equal to double to the from part b).

The diagram illustrates a mechanical setup involving a parabolic track. Here's a detailed description: - **Mass and Forces**: - A mass of 0.6 kg is placed at point A on a parabolic track. - Two springs are attached to the mass, each with a spring constant of 120 N/m. - **Dimensions**: - The horizontal distance from point A to point B is 1 meter, with each segment (A to O and O to B) measuring 0.5 meters. - The vertical distance from point A to the horizontal axis through point O is 0.25 meters. - Similarly, the vertical distance from point B to the horizontal axis through point O is also 0.25 meters. - **Track**: - The track between points A and B is parabolic in shape, providing a smooth curve for the mass to slide along. This setup is typically used to study the dynamics of masses on curved tracks, exploring concepts such as potential energy, kinetic energy, and harmonic motion due to the springs.
Transcribed Image Text:The diagram illustrates a mechanical setup involving a parabolic track. Here's a detailed description: - **Mass and Forces**: - A mass of 0.6 kg is placed at point A on a parabolic track. - Two springs are attached to the mass, each with a spring constant of 120 N/m. - **Dimensions**: - The horizontal distance from point A to point B is 1 meter, with each segment (A to O and O to B) measuring 0.5 meters. - The vertical distance from point A to the horizontal axis through point O is 0.25 meters. - Similarly, the vertical distance from point B to the horizontal axis through point O is also 0.25 meters. - **Track**: - The track between points A and B is parabolic in shape, providing a smooth curve for the mass to slide along. This setup is typically used to study the dynamics of masses on curved tracks, exploring concepts such as potential energy, kinetic energy, and harmonic motion due to the springs.
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