A cart, of mass m, is released at the top of a ramp of distance d and height h as shown. Neglect backwards friction and drag. Calculate the final speed (v) in each of the following cases. m [kg] h [m] d[m] V [m/s] 3 0.5 1.5 6 3 3 6 0.5 1.00 0.5 1.00 1.5 1.5 3.00 3.00 h reference level
A cart, of mass m, is released at the top of a ramp of distance d and height h as shown. Neglect backwards friction and drag. Calculate the final speed (v) in each of the following cases. m [kg] h [m] d[m] V [m/s] 3 0.5 1.5 6 3 3 6 0.5 1.00 0.5 1.00 1.5 1.5 3.00 3.00 h reference level
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![**Educational Content: Energy on an Inclined Plane**
A cart, of mass \( m \), is released at the top of a ramp with distance \( d \) and height \( h \) as illustrated. Assume that friction and drag are negligible.
**Objective:**
Calculate the final speed (\( v_f \)) of the cart in each scenario provided.
---
**Table of Values:**
| \( m \) [kg] | \( h \) [m] | \( d \) [m] | \( v_f \) [m/s] |
|--------------|-------------|-------------|-----------------|
| 3 | 0.5 | 1.5 | [ ] |
| 6 | 0.5 | 1.5 | [ ] |
| 3 | 1.0 | 1.5 | [ ] |
| 3 | 0.5 | 3.0 | [ ] |
| 6 | 1.0 | 3.0 | [ ] |
---
**Diagram Explanation:**
- The diagram shows a ramp inclined at an angle with a cart at the top and bottom of the incline.
- Distance \( d \) represents the length of the ramp from the top to the bottom.
- Height \( h \) indicates the vertical drop from the top to the bottom of the ramp.
- A “reference level” is marked at the bottom of the ramp.
---
**Conceptual Understanding:**
The potential energy at the top of the ramp transforms into kinetic energy at the bottom. Use the following energy conservation formula for calculation:
\[ mgh = \frac{1}{2}mv_f^2 \]
Where:
- \( m \) is the mass of the cart.
- \( g \) is the acceleration due to gravity (approx. \( 9.81 \, \text{m/s}^2 \)).
- \( h \) is the height of the ramp.
- \( v_f \) is the final speed of the cart at the bottom.
Solve for \( v_f \) to find the final speed of the cart using the given values.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb3775607-704b-46c9-9d82-255ef12a8c56%2F27466c15-06f4-4a2e-9405-5139adf9a049%2F3hoqanm_processed.png&w=3840&q=75)
Transcribed Image Text:**Educational Content: Energy on an Inclined Plane**
A cart, of mass \( m \), is released at the top of a ramp with distance \( d \) and height \( h \) as illustrated. Assume that friction and drag are negligible.
**Objective:**
Calculate the final speed (\( v_f \)) of the cart in each scenario provided.
---
**Table of Values:**
| \( m \) [kg] | \( h \) [m] | \( d \) [m] | \( v_f \) [m/s] |
|--------------|-------------|-------------|-----------------|
| 3 | 0.5 | 1.5 | [ ] |
| 6 | 0.5 | 1.5 | [ ] |
| 3 | 1.0 | 1.5 | [ ] |
| 3 | 0.5 | 3.0 | [ ] |
| 6 | 1.0 | 3.0 | [ ] |
---
**Diagram Explanation:**
- The diagram shows a ramp inclined at an angle with a cart at the top and bottom of the incline.
- Distance \( d \) represents the length of the ramp from the top to the bottom.
- Height \( h \) indicates the vertical drop from the top to the bottom of the ramp.
- A “reference level” is marked at the bottom of the ramp.
---
**Conceptual Understanding:**
The potential energy at the top of the ramp transforms into kinetic energy at the bottom. Use the following energy conservation formula for calculation:
\[ mgh = \frac{1}{2}mv_f^2 \]
Where:
- \( m \) is the mass of the cart.
- \( g \) is the acceleration due to gravity (approx. \( 9.81 \, \text{m/s}^2 \)).
- \( h \) is the height of the ramp.
- \( v_f \) is the final speed of the cart at the bottom.
Solve for \( v_f \) to find the final speed of the cart using the given values.
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