Vertical circular motion, "up-side-down," apparent weight: On a roller coaster, al point of the inside of the loop-the-loop, your apparent weight (the normal force on you from the seat) is equal to only half your weight. Assume that your body of mass m travels in a vertical circle with radius r, and that your speed v remains constant. (See PSL 6.11,12) a) Draw a FBD of you (i) at the top, and (ii) at the bottom of the loop. b) Determine your tangential speed at the top. c) Determine your apparent weight at the bottom. d) If instead your apparent weight at the top were zero (i.e., you are on the verge of falling out), what is the speed? e) Determine all these values if your mass is 100 kg and the radius is 5.00 m.
Vertical circular motion, "up-side-down," apparent weight: On a roller coaster, al point of the inside of the loop-the-loop, your apparent weight (the normal force on you from the seat) is equal to only half your weight. Assume that your body of mass m travels in a vertical circle with radius r, and that your speed v remains constant. (See PSL 6.11,12) a) Draw a FBD of you (i) at the top, and (ii) at the bottom of the loop. b) Determine your tangential speed at the top. c) Determine your apparent weight at the bottom. d) If instead your apparent weight at the top were zero (i.e., you are on the verge of falling out), what is the speed? e) Determine all these values if your mass is 100 kg and the radius is 5.00 m.
Please do parts b c & d
This is a practice problem not homework
Transcribed Image Text:### Vertical Circular Motion, "Up-Side-Down," Apparent Weight
**Scenario:** On a roller coaster, at the very top point of the inside of the loop-the-loop, your apparent weight (the normal force on you from the seat) is equal to only half your weight. Assume that your body of mass \( m \) travels in a vertical circle with radius \( r \), and that your speed \( v \) remains constant.
**Tasks:**
a) **Draw a Free Body Diagram (FBD) at the Top and Bottom of the Loop:**
- **Diagram (i)** (at the top): Shows forces acting downward, including gravitational force \( mg \) and normal force \( FN \).
- **Diagram (ii)** (at the bottom): Shows gravitational force \( mg \) acting downward and normal force \( FN \) acting upward.
b) **Determine Your Tangential Speed at the Top:**
\[
V_{\text{tan}} = \frac{2\pi r}{T}
\]
\[
mg = \frac{ma}{2} \implies a = \frac{mg}{2m} = \frac{g}{2}
\]
\[
a_c = \frac{v^2}{r}
\]
c) **Determine Your Apparent Weight at the Bottom:**
\[
F_{\text{net}} = \frac{mv^2}{r}
\]
d) **If Instead Your Apparent Weight at the Top Were Zero:**
\[
Rg = \frac{v^2}{r} \implies V_{\text{tan}} = \sqrt{\frac{Rg}{2}}
\]
e) **Determine All These Values if Your Mass is 100 kg and the Radius is 5.0 m.**
**Explanation:**
- **Diagram Explanation:** The circular diagram shows the roller coaster at the top and bottom of the loop, indicating the direction of forces. At the top, both gravitational force and normal force point downward. At the bottom, gravitational force points downward while normal force points upward.
- **Equations and Calculations:** The calculations use the principles of circular motion to derive tangential speed and apparent weight. The equations involve substituting given variables into standard formulas for centripetal acceleration and force.
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![### Vertical Circular Motion, "Up-Side-Down," Apparent Weight
**Scenario:** On a roller coaster, at the very top point of the inside of the loop-the-loop, your apparent weight (the normal force on you from the seat) is equal to only half your weight. Assume that your body of mass \( m \) travels in a vertical circle with radius \( r \), and that your speed \( v \) remains constant.
**Tasks:**
a) **Draw a Free Body Diagram (FBD) at the Top and Bottom of the Loop:**
- **Diagram (i)** (at the top): Shows forces acting downward, including gravitational force \( mg \) and normal force \( FN \).
- **Diagram (ii)** (at the bottom): Shows gravitational force \( mg \) acting downward and normal force \( FN \) acting upward.
b) **Determine Your Tangential Speed at the Top:**
\[
V_{\text{tan}} = \frac{2\pi r}{T}
\]
\[
mg = \frac{ma}{2} \implies a = \frac{mg}{2m} = \frac{g}{2}
\]
\[
a_c = \frac{v^2}{r}
\]
c) **Determine Your Apparent Weight at the Bottom:**
\[
F_{\text{net}} = \frac{mv^2}{r}
\]
d) **If Instead Your Apparent Weight at the Top Were Zero:**
\[
Rg = \frac{v^2}{r} \implies V_{\text{tan}} = \sqrt{\frac{Rg}{2}}
\]
e) **Determine All These Values if Your Mass is 100 kg and the Radius is 5.0 m.**
**Explanation:**
- **Diagram Explanation:** The circular diagram shows the roller coaster at the top and bottom of the loop, indicating the direction of forces. At the top, both gravitational force and normal force point downward. At the bottom, gravitational force points downward while normal force points upward.
- **Equations and Calculations:** The calculations use the principles of circular motion to derive tangential speed and apparent weight. The equations involve substituting given variables into standard formulas for centripetal acceleration and force.](https://content.bartleby.com/qna-images/question/9d3c3ab0-3648-4520-b7d5-a83f201d4237/17d0a3f2-abc8-4c82-b7bb-0049da5f5806/18aqgv8_processed.jpeg)
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