Constrained to move Horizontally

  • Thread starter Sheen91
  • Start date
In summary, the conversation discusses the use of the formula v = \dot{r} \hat{r} + r\dot{\vartheta} \hat{\vartheta} to solve for the unknown variable \dot{r}. The conversation also mentions the conversion from polar coordinates to Cartesian coordinates, and suggests decomposing v into components in the orthogonal directions \hat{r} and \hat{\vartheta}.
  • #1
Sheen91
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Homework Statement



[PLAIN]http://img231.imageshack.us/img231/636/question2m.jpg [Broken]

Homework Equations



v = [tex]\dot{r}[/tex] [tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex] [tex]\hat{\vartheta}[/tex]

The Attempt at a Solution



[tex]\dot{r}[/tex] = ?
\vartheta = 80°
v = 55mm/s

So I guess I just use the formula above.

v = [tex]\dot{r}[/tex] [tex]\hat{r}[/tex] + r[tex]\dot{\vartheta}[/tex] [tex]\hat{\vartheta}[/tex]

55² = [tex]\dot{r}[/tex]² + rΘ'

And so you try and solve for [tex]\dot{r}[/tex]

r'² = 55² - (r*Θ')²
r' = sqrt(55² - (r*Θ')²)

And then I get stuck. I am either missing something. Or not doing something right. I guess this isn't really r theta, it is more a conversion from r theta to x-y.

Not 100% sure how to do that though.

Cheers
 
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  • #2
first you can write sevreal expresisons in tex as follows
[tex]\vec{v} = \dot{r} \hat{r} + r \dot{\vartheta}\hat{\vartheta}[/tex]

so knowing theta and |v| you should be able to decompose v into components in the orthogonal directions [itex]\hat{r}, \hat{\vartheta}[/itex]
 
  • #3
I manage to get the question.

Thanks :D
 

1. How does being constrained to move horizontally affect an object's motion?

Being constrained to move horizontally means that an object can only move in a straight line along the horizontal axis. This affects the object's motion by limiting its range of motion and preventing it from moving in any other direction.

2. What types of forces can cause an object to be constrained to move horizontally?

There are various types of forces that can cause an object to be constrained to move horizontally. These include frictional forces, tension forces, and normal forces. For example, a block sliding on a horizontal surface is constrained by frictional forces.

3. How does the angle of the horizontal constraint affect an object's motion?

The angle of the horizontal constraint can greatly affect an object's motion. If the constraint is perfectly horizontal, the object will only be able to move in a straight line along the horizontal axis. However, if the constraint is at an angle, the object's motion will be influenced by both horizontal and vertical forces.

4. Can an object be constrained to move horizontally and vertically at the same time?

Yes, an object can be constrained to move horizontally and vertically at the same time. This can occur if there are two separate constraints acting on the object, one restricting horizontal motion and the other restricting vertical motion. In this case, the object's motion will be a combination of both horizontal and vertical movements.

5. How does the mass of an object affect its motion when constrained to move horizontally?

The mass of an object does not directly affect its motion when constrained to move horizontally. However, the object's mass can influence the amount of force needed to overcome the constraint and move the object. For example, a heavier object may require more force to overcome friction and move along a horizontal surface.

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