Safely Negotiating Unbanked Curves: Slowing Car Speed for Safety

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In summary: So, if you divide v by 3, you get v prime. Therefore, the driver must slow the car down to one third of its original speed, or 7.67 m/s, in order to continue safely around the curve. In summary, the maximum static frictional force acting on the tires while a car is safely negotiating an unbanked circular turn at a speed of 23 m/s is reduced by a factor of three due to a wet patch on the road. To continue safely around the curve, the driver must slow the car down to one third of its original speed, or 7.67 m/s. The equation \mu_s(g) = v^2/r must be balanced by dividing both sides by three
  • #1
quickclick330
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A car is safely negotiating an unbanked circular turn at a speed of 23 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static friction force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?

i have it so where mu_s = v^2/r but I don't know if that's right, help please! thanks :-)
 
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  • #2
quickclick330 said:
A car is safely negotiating an unbanked circular turn at a speed of 23 m/s. The maximum static frictional force acts on the tires. Suddenly a wet patch in the road reduces the maximum static friction force by a factor of three. If the car is to continue safely around the curve, to what speed must the driver slow the car?

i have it so where mu_s = v^2/r but I don't know if that's right, help please! thanks :-)
I think you mean mu_s(g) = v^2/r. But in any case, if mu_s is reduced by 3, then v^2 must be reduced by what factor to keep the car from slipping?
 
  • #3
3/r maybe?
 
  • #4
The radius of the turn is constant. If you divide [tex]\mu_s[/tex] by 3, what must you do to balance your equation?
 
  • #5
then you must divide the other side of the equation to balance it, so would it be ((v^2/r)/3)?
 
  • #6
Exactly. But the only thing you're allowed to change is v.
What should you do to v to get the whole expression to equal [tex]{\frac{v^2}{3r}[/tex]?
 
  • #7
I'm not sure...not having the radius measurement is throwing me off
 
  • #8
It doesn't matter what the radius is. It doesn't change.
You have [tex]\frac{v^2}{r}[/tex]
You need to divide all of that by three, but you're NOT allowed to touch r. All you're allowed to change is v. What might you do to v so that

[tex]\frac{v^2}{3r}=\frac{(v')^2}{r}[/tex] ?
 
  • #9
I tried to divide by 3 again...what is v prime??
 
  • #10
quickclick330 said:
I tried to divide by 3 again...what is v prime??

The speed the driver must slow down to in order to continue along the curve safely. This is what you are trying to solve for.
 
  • #11
quickclick330 said:
I tried to divide by 3 again...what is v prime??

v prime is your new velocity. The one that makes the origianl exprssion (v^2/r) get divided by 3.
 

1. What are unbanked curves?

Unbanked curves are turns on a road or track that do not have a slope or angle built into them to help vehicles navigate the curve. This means that the road surface is flat and does not provide any assistance in keeping a vehicle on the road.

2. Why is it important to slow car speed on unbanked curves?

Slowing car speed on unbanked curves is important because it helps to reduce the risk of accidents and increase safety for both the driver and other road users. Unbanked curves are more difficult to navigate at high speeds and slowing down can help prevent loss of control and potential crashes.

3. How can car speed be safely slowed on unbanked curves?

There are a few ways to safely slow car speed on unbanked curves. One method is to apply gentle braking while approaching the curve and continue to gradually decrease speed as you navigate the curve. Another method is to downshift to a lower gear to reduce speed without using the brakes. It is important to maintain a consistent speed and avoid sudden or aggressive braking, as this can also cause loss of control on unbanked curves.

4. Is it necessary to slow down on all unbanked curves?

Yes, it is necessary to slow down on all unbanked curves. Even if the curve appears to be gentle or easy to navigate, it is still important to reduce speed as a precaution. Unbanked curves can be unpredictable and it is better to err on the side of caution to ensure safety.

5. What are the consequences of not slowing down on unbanked curves?

The consequences of not slowing down on unbanked curves can be severe. It can lead to loss of control, rollovers, collisions with other vehicles or objects, and even fatalities. Speeding on unbanked curves is a common cause of accidents, so it is important to always follow recommended speed limits and slow down for safety on these types of curves.

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