As shown below, a mass of 10 kg placed on a ramp is in contact with a spring. The spring has a stiffness constant of k 2000 N/m. There is a coefficient of kinetic friction 4k between the mass and the ramp equal to 0.3 and so some energy will be lost as the mass slides. The angle of the ramp is 30 degrees with respect to the horizontal and the distance marked d is 4 meters. If the spring is compressed by a length of I meter (as shown) and then released, how far will the mass travel from the edge of the ramp (marked R) before it hits the ground? Ignore air resistance and g 9.8m/s².,

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Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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**Transcription:**

As shown below, a mass of 10 kg placed on a ramp is in contact with a spring. The spring has a stiffness constant of \( k = 2000 \, \text{N/m} \). There is a coefficient of kinetic friction \( \mu_k \) between the mass and the ramp equal to 0.3, and so some energy will be lost as the mass slides. The angle of the ramp is 30 degrees with respect to the horizontal, and the distance marked \( d \) is 4 meters.

If the spring is compressed by a length of 1 meter (as shown) and then released, how far will the mass travel from the edge of the ramp (marked \( R \)) before it hits the ground? Ignore air resistance and \( g = 9.8 \, \text{m/s}^2 \).

**Diagram Explanation:**

- The diagram depicts a mass on a ramp with a spring compressed behind it.
- The spring is compressed and positioned at the bottom of the ramp, exerting a force on the mass.
- The mass slides up the ramp, which is inclined at a 30-degree angle from the horizontal.
- The distance \( d \), which is 4 meters, is marked from the spring compression point to the top of the ramp.
- The horizontal distance \( R \) represents how far the mass will travel once it leaves the ramp and hits the ground.
- The ramp system indicates how energy is transferred and transformed as the mass moves due to the spring's force, taking into account the effects of friction.
Transcribed Image Text:**Transcription:** As shown below, a mass of 10 kg placed on a ramp is in contact with a spring. The spring has a stiffness constant of \( k = 2000 \, \text{N/m} \). There is a coefficient of kinetic friction \( \mu_k \) between the mass and the ramp equal to 0.3, and so some energy will be lost as the mass slides. The angle of the ramp is 30 degrees with respect to the horizontal, and the distance marked \( d \) is 4 meters. If the spring is compressed by a length of 1 meter (as shown) and then released, how far will the mass travel from the edge of the ramp (marked \( R \)) before it hits the ground? Ignore air resistance and \( g = 9.8 \, \text{m/s}^2 \). **Diagram Explanation:** - The diagram depicts a mass on a ramp with a spring compressed behind it. - The spring is compressed and positioned at the bottom of the ramp, exerting a force on the mass. - The mass slides up the ramp, which is inclined at a 30-degree angle from the horizontal. - The distance \( d \), which is 4 meters, is marked from the spring compression point to the top of the ramp. - The horizontal distance \( R \) represents how far the mass will travel once it leaves the ramp and hits the ground. - The ramp system indicates how energy is transferred and transformed as the mass moves due to the spring's force, taking into account the effects of friction.
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