An orange block of mass 2.5 kg is on an inclined plane. There is no friction between the block and the plane except in the region shown in red and black on the diagram above.  The plane is inclined at an angle of θ = 17 degrees above horizontal. The block begins at rest, leaning against a spring with a spring constant of k = 741 newtons per meter.  At the start, the spring has a compressed length of x1 = 0.39 meters.  The spring then expands to its equilibrium length of x2 = 0.65 meters, sending the block sliding up the ramp. The block has no friction with the plane except in the single region of length L = 0.78 meters, shown in red and black above. The coefficient of kinetic friction between the block and this region is μ K = 0.24. The block slides past this region and continues up the plane. What is the speed of the block, in units of meters per second, when it has slid a distance d = 1.3 meters along the plane from the place where it started? (This is the distance measured from the position when the spring was still compressed.)

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An orange block of mass 2.5 kg is on an inclined plane. There is no friction between the block and the plane except in the region shown in red and black on the diagram above.  The plane is inclined at an angle of θ = 17 degrees above horizontal.

The block begins at rest, leaning against a spring with a spring constant of k = 741 newtons per meter.  At the start, the spring has a compressed length of x1 = 0.39 meters.  The spring then expands to its equilibrium length of x2 = 0.65 meters, sending the block sliding up the ramp.

The block has no friction with the plane except in the single region of length L = 0.78 meters, shown in red and black above. The coefficient of kinetic friction between the block and this region is μ K = 0.24. The block slides past this region and continues up the plane.

What is the speed of the block, in units of meters per second, when it has slid a distance = 1.3 meters along the plane from the place where it started? (This is the distance measured from the position when the spring was still compressed.)

The image consists of two diagrams illustrating a block on an inclined plane, both labeled "Before" and "After."

**Top Diagram (Before):**

- A block is positioned on an inclined plane supported by a compressed spring.
- The spring is compressed by a distance labeled \(x_1\).
- The block is at rest before it moves.
- The distance from the starting point to the block's stopping point on the ramp is labeled \(L\).

**Bottom Diagram (After):**

- The block has moved up the inclined plane due to the release of the spring's energy.
- The new compression of the spring is labeled \(x_2\), indicating a potential change in spring compression.
- The distance the block has moved from its initial position is labeled \(d\).
- The block comes to rest further up the ramp than in the first diagram.

Both diagrams convey the concept of potential energy stored in a spring and the subsequent conversion of this energy into kinetic energy, causing motion along the inclined plane. The diagrams are useful for explaining principles in physics related to energy transformation and motion on inclined planes.
Transcribed Image Text:The image consists of two diagrams illustrating a block on an inclined plane, both labeled "Before" and "After." **Top Diagram (Before):** - A block is positioned on an inclined plane supported by a compressed spring. - The spring is compressed by a distance labeled \(x_1\). - The block is at rest before it moves. - The distance from the starting point to the block's stopping point on the ramp is labeled \(L\). **Bottom Diagram (After):** - The block has moved up the inclined plane due to the release of the spring's energy. - The new compression of the spring is labeled \(x_2\), indicating a potential change in spring compression. - The distance the block has moved from its initial position is labeled \(d\). - The block comes to rest further up the ramp than in the first diagram. Both diagrams convey the concept of potential energy stored in a spring and the subsequent conversion of this energy into kinetic energy, causing motion along the inclined plane. The diagrams are useful for explaining principles in physics related to energy transformation and motion on inclined planes.
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