Distance Traveled (Fired by a Spring) The box below has a mass of 172 g and is placed against a spring with a spring constant of 16.6 N/m. The box is then pushed into the spring until the spring has been compressed 181 mm. The box is held at rest for a few seconds and then released so that all the stored energy in the spring is converted into kinetic energy for the box. After leaving the spring the box encounters a surface with a coefficient of friction of 0.46. How far will the block travel before all the kinetic energy of the block has been converted to heat by this friction End 181 mm k = 16.60 N/m μ = 0.46 172 g
Distance Traveled (Fired by a Spring) The box below has a mass of 172 g and is placed against a spring with a spring constant of 16.6 N/m. The box is then pushed into the spring until the spring has been compressed 181 mm. The box is held at rest for a few seconds and then released so that all the stored energy in the spring is converted into kinetic energy for the box. After leaving the spring the box encounters a surface with a coefficient of friction of 0.46. How far will the block travel before all the kinetic energy of the block has been converted to heat by this friction End 181 mm k = 16.60 N/m μ = 0.46 172 g
Transcribed Image Text:### Distance Traveled (Fired by a Spring)
**Scenario Overview:**
The box in the diagram has a mass of 172 g and is placed against a spring with a spring constant of 16.6 N/m. The box is pushed into the spring until the spring has been compressed by 181 mm. It is then held at rest for a few seconds and released. Upon release, all the stored energy in the spring is converted into kinetic energy for the box.
**Problem Statement:**
After leaving the spring, the box encounters a surface with a coefficient of friction (μ) of 0.46. The question posed is: How far will the block travel before all the kinetic energy of the block has been converted to heat by this friction?
**Diagram & Description:**
1. **Spring and Box Initial Position:**
- The spring's force constant (k) is 16.6 N/m.
- The box has a mass of 172 g.
- The spring is compressed by a distance of 181 mm.
2. **Surface with Friction:**
- The box slides over a surface with a coefficient of friction (μ) equal to 0.46.
**Objective:**
Determine the distance the box will travel on this surface before coming to a stop due to friction converting all its kinetic energy into heat.
**Understanding the Diagram:**
The diagram at the bottom displays:
- A spring connected to a block.
- The block's mass labeled as 172 g.
- The compression distance of the spring is 181 mm.
- The coefficient of friction (μ) between the block and the surface is 0.46.
- The surface the box travels on is depicted with varying colors, indicating the path of the box from compression to the 'End' point where friction brings it to a stop.
This problem involves applying principles of energy conversion, where potential energy stored in the compressed spring converts to kinetic energy, which then is dissipated as heat through friction as the box moves. Calculations would involve equating these energy transitions to solve for the distance traveled.
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