A spring (k = 75.0 N/m) has a natural length of 1.00 m. The spring is compressed to a length of 0.500 m and a block of mass 1.50 kg is attached at its free end on a frictionless slope which makes an angle of 41.0° with respect to the horizontal as shown in the figure below. The spring is then released from rest. How far up the slope from the starting position will the block move up the incline before coming to rest? 0,50 m e =41° 2m The incline is cut so that the length of the incline is now 1 m. How much should the spring be compressed if the block needs to hit an object 2 m away?

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Chapter1: Units, Trigonometry. And Vectors
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### Problem 2

A spring (k = 75.0 N/m) has a natural length of 1.00 m. The spring is compressed to a length of 0.500 m and a block of mass 1.50 kg is attached at its free end on a frictionless slope which makes an angle of 41.0° with respect to the horizontal as shown in the figure below. The spring is then released from rest. **How far up the slope from the starting position will the block move up the incline before coming to rest?**

#### Diagram Explanation

In the provided diagram, a spring is compressed and attached to a block on a frictionless incline. The incline makes an angle of 41° with the horizontal.

- The compressed length of the spring is labeled as 0.50 m.
- The incline is clearly marked with the angle θ = 41°.
- A horizontal line at the bottom of the diagram indicates a length of 2m.

Below the diagram, an additional question is presented:

#### Additional Question

The incline is cut so that the length of the incline is now 1 m. **How much should the spring be compressed if the block needs to hit an object 2 m away?**

---

Graphical or computational steps would typically follow to solve for the potential energy stored in the compressed spring, equate it to the gravitational potential energy when the block moves up the slope, and solve for the distance traveled or the new compression length of the spring.
Transcribed Image Text:### Problem 2 A spring (k = 75.0 N/m) has a natural length of 1.00 m. The spring is compressed to a length of 0.500 m and a block of mass 1.50 kg is attached at its free end on a frictionless slope which makes an angle of 41.0° with respect to the horizontal as shown in the figure below. The spring is then released from rest. **How far up the slope from the starting position will the block move up the incline before coming to rest?** #### Diagram Explanation In the provided diagram, a spring is compressed and attached to a block on a frictionless incline. The incline makes an angle of 41° with the horizontal. - The compressed length of the spring is labeled as 0.50 m. - The incline is clearly marked with the angle θ = 41°. - A horizontal line at the bottom of the diagram indicates a length of 2m. Below the diagram, an additional question is presented: #### Additional Question The incline is cut so that the length of the incline is now 1 m. **How much should the spring be compressed if the block needs to hit an object 2 m away?** --- Graphical or computational steps would typically follow to solve for the potential energy stored in the compressed spring, equate it to the gravitational potential energy when the block moves up the slope, and solve for the distance traveled or the new compression length of the spring.
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