Finding acceleration with circular motion

[David Mordigal]

Homework Statement

Entrance and exit ramps for freeways are often circular stretches of road. As you go around one at a constant speed, you will experience a constant acceleration. Suppose you drive through an entrance ramp at a modest speed and your acceleration is 2.0 m/s².

What will be the acceleration if you triple your speed?

Express your answer to two significant figures and include the appropriate units.

Homework Equations

a = v²/R

The Attempt at a Solution

Given that the initial acceleration is 2.0 m/s², and a = v²/R...

I am not sure where to get started. R is not given, and v is not given. I know how to find a theoretically, but since I do not have concrete values to start with besides acceleration, I do not know where to begin.

Thanks for any guidance.

 

[Chestermiller]

Try this with R = 50 m, and with whatever velocity you need to give you a = 2 m/s². Now, if you triple v, what do you get for a?

Chet

 

[Konoha]

You don't actually need any more information, as you wrote yourself in a circular motion a = v2/R. now imagine, R is constant (because you are in the same road), you triple the speed, what will happen to acceleration?

 

[David Mordigal]

OK, I got it. Thanks all for your help!

 

[HalfLostAndSearching]

I would approach this problem by first identifying the known and unknown variables. In this case, the known variable is the initial acceleration (2.0 m/s2) and the unknown variable is the acceleration when the speed is tripled.

From the given information, we can also deduce that the speed is directly proportional to the acceleration (as the speed increases, the acceleration also increases). Therefore, if the speed is tripled, the acceleration will also triple.

To solve for the unknown acceleration, we can use the equation a = v2/R. Since we do not have the values for v and R, we can use a general approach and express the unknown acceleration as a multiple of the initial acceleration.

Let's say the initial speed is v1 and the initial radius is R1. Then, the initial acceleration can be expressed as a1 = v1^2/R1.

If the speed is tripled, the new speed will be 3v1, and the acceleration will be a2 = (3v1)^2/R1 = 9v1^2/R1.

Therefore, the new acceleration (a2) is 9 times the initial acceleration (a1). Thus, we can express the new acceleration as a2 = 9a1.

Plugging in the value of a1 = 2.0 m/s2, we get a2 = 9(2.0) = 18.0 m/s2.

Hence, the acceleration when the speed is tripled is 18.0 m/s2.

To express the answer in two significant figures, we can round it to 18 m/s2.

Therefore, the acceleration when the speed is tripled is 18 m/s2.

Note: It is important to note that this approach is a simplified method and may not be applicable in all cases. In a real-world scenario, we would need to know the actual values of speed and radius to accurately calculate the acceleration.