A block with mass m = 1.14 kg is placed against a spring on a frictionless incline with angle = 22.0° (see the figure). (The block is not attached to the spring.) The spring, with spring constant k = 15 N/cm, is compressed 24.1 cm and then released. (a) What is the elastic potential energy of the compressed spring? (b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline? (c) How far along the incline is the highest point from the release point?

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A block with mass \( m = 1.14 \, \text{kg} \) is placed against a spring on a frictionless incline with angle \( \theta = 22.0^\circ \) (see the figure). The block is not attached to the spring. The spring, with a spring constant \( k = 15 \, \text{N/cm} \), is compressed \( 24.1 \, \text{cm} \) and then released. 

(a) What is the elastic potential energy of the compressed spring?

(b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline?

(c) How far along the incline is the highest point from the release point?

**Diagram Explanation:**

The diagram shows a green block labeled "m" on a gray incline, which forms an angle \( \theta \) with the horizontal. A spring with compression labeled "x" is positioned at the bottom of the incline with the block initially placed against it. The incline is shown as frictionless. The compression displaces the block up the incline when released.
Transcribed Image Text:A block with mass \( m = 1.14 \, \text{kg} \) is placed against a spring on a frictionless incline with angle \( \theta = 22.0^\circ \) (see the figure). The block is not attached to the spring. The spring, with a spring constant \( k = 15 \, \text{N/cm} \), is compressed \( 24.1 \, \text{cm} \) and then released. (a) What is the elastic potential energy of the compressed spring? (b) What is the change in the gravitational potential energy of the block-Earth system as the block moves from the release point to its highest point on the incline? (c) How far along the incline is the highest point from the release point? **Diagram Explanation:** The diagram shows a green block labeled "m" on a gray incline, which forms an angle \( \theta \) with the horizontal. A spring with compression labeled "x" is positioned at the bottom of the incline with the block initially placed against it. The incline is shown as frictionless. The compression displaces the block up the incline when released.
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