What equation is used to calculate the speed, v, up the plane?

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A block of mass m is attached to a spring (constant k), sliding on a frictionless incline (angle theta), with respect to the horizontal. The spring begins compressed at a distance x and is released from rest. The block travels past an equilibrium point (point B) and has speed v, traveling up the plane. What equation is used to calculate the speed, v, up the plane?

The image illustrates a physics problem involving a mass-spring system on an inclined plane. Here's a detailed explanation:

1. **Inclined Plane**: The plane is inclined at an angle \(\theta\) to the horizontal.

2. **Spring and Mass**: 
   - A spring with spring constant \(k\) is attached to an object with mass \(m\). The spring is positioned parallel to the inclined plane.
   - The object is situated at a distance \(x\) up the inclined plane from the spring's relaxed position.

3. **Position and Labeling**:
   - The object is shown compressing the spring toward the inclined plane’s base.
   - A dotted line extends from the object's initial position to indicate Point \(B\), further up the incline.

This setup can be used to analyze the forces acting on the mass and the potential energy in the spring. Common topics related to this diagram include harmonic motion on an incline, energy conservation, and the analysis of forces along inclined surfaces.
Transcribed Image Text:The image illustrates a physics problem involving a mass-spring system on an inclined plane. Here's a detailed explanation: 1. **Inclined Plane**: The plane is inclined at an angle \(\theta\) to the horizontal. 2. **Spring and Mass**: - A spring with spring constant \(k\) is attached to an object with mass \(m\). The spring is positioned parallel to the inclined plane. - The object is situated at a distance \(x\) up the inclined plane from the spring's relaxed position. 3. **Position and Labeling**: - The object is shown compressing the spring toward the inclined plane’s base. - A dotted line extends from the object's initial position to indicate Point \(B\), further up the incline. This setup can be used to analyze the forces acting on the mass and the potential energy in the spring. Common topics related to this diagram include harmonic motion on an incline, energy conservation, and the analysis of forces along inclined surfaces.
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