tic energy at the bott . If the cart coasts fro s the cart go as mea

College Physics
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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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#2 please show work so I can understand. Thank you! 

**Physics Homework: Energy and Motion**

**2. Refer to figure 2. The 10.0 kg green cart travels down a ramp — from point A to B. Calculate its starting potential energy, kinetic energy at the bottom of the ramp, and its velocity coming off the bottom of the ramp. If the cart coasts from points B to C, did it do any work? How far up the 2nd ramp does the cart go as measured from the ground?**

*Figure 2:*

- **Description:** This figure depicts a cart initially placed at point A on the first ramp and traveling down to point B at the base of the first ramp. Subsequently, it coasts horizontally from point B to point C and up the second ramp.
- **Details:**
  - Point A is positioned 10.0 m above the ground level before descending the sloped ramp to point B.
  - The two ramps form right angles with the ground, creating a triangular shape with the horizontal ground line which extends from B to C at the base.
  - From C, the second ramp rises at the same angle as the first but in the opposite direction.

**3. Refer to figure 3. How fast must the cart go in order to complete the loop-to-loop successfully?**

*Figure 3:*

- **Description:** This figure illustrates a green cart approaching a loop-the-loop structure.
- **Details:**
  - The loop has a diameter of 20.0 meters.
  - The diameter is prominently displayed by a vertical line measuring 20.0 meters.
  - The cart is assumed to approach the loop from a flat horizontal track.

**Considerations for Calculations:**

1. Potential Energy at A (PE): 
   \[
   PE = mgh
   \]
   where:  
   \( m \) = 10.0 kg (mass of the cart)  
   \( g \) = 9.8 m/s² (acceleration due to gravity)  
   \( h \) = 10.0 m (height at point A)

2. Kinetic Energy at B and Velocity: 
   Because all potential energy converts into kinetic energy at the bottom of the ramp:
   \[
   KE = PE
   \]
   The kinetic energy (KE) at point B can be calculated using:
   \[
   KE = \frac{1}{2}mv^2
Transcribed Image Text:**Physics Homework: Energy and Motion** **2. Refer to figure 2. The 10.0 kg green cart travels down a ramp — from point A to B. Calculate its starting potential energy, kinetic energy at the bottom of the ramp, and its velocity coming off the bottom of the ramp. If the cart coasts from points B to C, did it do any work? How far up the 2nd ramp does the cart go as measured from the ground?** *Figure 2:* - **Description:** This figure depicts a cart initially placed at point A on the first ramp and traveling down to point B at the base of the first ramp. Subsequently, it coasts horizontally from point B to point C and up the second ramp. - **Details:** - Point A is positioned 10.0 m above the ground level before descending the sloped ramp to point B. - The two ramps form right angles with the ground, creating a triangular shape with the horizontal ground line which extends from B to C at the base. - From C, the second ramp rises at the same angle as the first but in the opposite direction. **3. Refer to figure 3. How fast must the cart go in order to complete the loop-to-loop successfully?** *Figure 3:* - **Description:** This figure illustrates a green cart approaching a loop-the-loop structure. - **Details:** - The loop has a diameter of 20.0 meters. - The diameter is prominently displayed by a vertical line measuring 20.0 meters. - The cart is assumed to approach the loop from a flat horizontal track. **Considerations for Calculations:** 1. Potential Energy at A (PE): \[ PE = mgh \] where: \( m \) = 10.0 kg (mass of the cart) \( g \) = 9.8 m/s² (acceleration due to gravity) \( h \) = 10.0 m (height at point A) 2. Kinetic Energy at B and Velocity: Because all potential energy converts into kinetic energy at the bottom of the ramp: \[ KE = PE \] The kinetic energy (KE) at point B can be calculated using: \[ KE = \frac{1}{2}mv^2
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