Uniform Circular Motion Question (Mechanics/Physics I)

In summary: What are they?In summary, the conversation discusses a car traveling at a uniform speed in a circular path and the calculations for its acceleration and average speed. The attempted solution for part C involves calculating the average acceleration using the change in velocity over time, but the correct method would involve expressing the acceleration in terms of polar coordinates and using the x and y components of the change in velocity.
  • #1
adamwest
10
1
Uniform Circular Motion Question Please Help! (Mechanics/Physics I)

A car initially traveling eastward turns north by traveling in a circular path at uniform speed as in Figure P6.10. The length of the arc ABC is 200 m, and the car completes the turn in 34.0 s.

(figure attached as "visual.gif")

Figure P6.10
(a) What is the acceleration when the car is at B located at an angle of 35.0°? Express your answer in terms of the unit vectors i and j.
(b) Determine the car's average speed.
(c) Determine its average acceleration during the 34.0 s and express your answer in terms of the unit vectors i and j.


I have properly solved Parts A and B. It is only Part C that I am having trouble with.

Relevant equation is probably just a avg = Δv/Δt

The Attempt at a Solution



Part A: -.2224i m/s^2 + .1558j m/s^2(This is correct)
Part B: 5.88 m/s (This is correct)

Part C: I have tried the following:

a avg = Δv/Δt, and Δv = ((5.88)^2 + (5.88)^2)^1/2 = 8.3189 m/s ==> a avg = (8.3189/34.0 s) = .2447 m/s^2 (not correct)

and

a avg = Δv/Δt, and Δv=(r/t) since it is circular motion and over 34 seconds the change in both x and y are equal to the radius. So Δv= (127.3240 m / 34.0 s) = 3.7448 m/s ==> a avg = Δv/Δt, so a avg = (3.7448 m/s / 34.0 s) = .1101 m/s^2 for both i and j (not correct).

I know I am overlooking something really simple here. I also realize that the signs will be different for i and j, just as they were in part A. Please help! :)
 

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  • #2
Express ax and ay accelerations in terms of polar coordinates R and θ.

Then, average x accel = ax = ∫axdt/∫dt
and same for average y accel ay.

Then avg accel = a = ax i + ay j.
 
  • #3
adamwest said:
a avg = Δv/Δt, and Δv = ((5.88)^2 + (5.88)^2)^1/2
As rude man points out, the acceleration should be a vector. Your a avg = Δv/Δt is correct, but Δv is a vector.
Δv=(r/t) since it is circular motion and over 34 seconds the change in both x and y are equal to the radius.
Good observation, but think about the x and y components of Δv. I.e. the change in vx and the change in vy.
 

1. What is uniform circular motion?

Uniform circular motion refers to the movement of an object along a circular path at a constant speed.

2. What is the difference between uniform circular motion and simple harmonic motion?

The main difference between uniform circular motion and simple harmonic motion is that in uniform circular motion, the object moves along a circular path, while in simple harmonic motion, the object moves back and forth along a straight line.

3. What is the centripetal force in uniform circular motion?

The centripetal force is the force that keeps an object moving in a circular path. It always acts towards the center of the circle and is equal to the mass of the object multiplied by its velocity squared divided by the radius of the circle.

4. How is angular velocity related to linear velocity in uniform circular motion?

Angular velocity and linear velocity are directly proportional in uniform circular motion. This means that as the angular velocity increases, the linear velocity also increases, and vice versa.

5. How does the radius of the circle affect the centripetal force in uniform circular motion?

The radius of the circle is inversely proportional to the centripetal force in uniform circular motion. This means that as the radius increases, the centripetal force decreases, and vice versa.

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