Centripetal Acceleration of car

In summary, the problem involves two cars driving around in circles at constant speeds. Car B's circle is twice as large as car A's, but its centripetal acceleration is three times as large. Using the equation a=(v^2/r) for centripetal acceleration, the answer can be found by writing equations for the centripetal accelerations of both cars, and then solving for the relation between their velocities. The answer is that car B is driving 2.45 times faster than car A.
  • #1
bgrove
1
0

Homework Statement


Two cars drive around in circles at constant speeds. Car B's circle is twice as large as car A's, but its centripetal acceleration is three times as large. How many times faster is car B driving than car A?

Homework Equations


I'm trying to use a=(v^2/r) for centripetal acceleration.

The Attempt at a Solution


I don't really know where to start on this one.

Per our answer key, the answer should be: 2.45 times faster.
 
Physics news on Phys.org
  • #2
You want to find a relation between the velocity of car A and car B, and you're given a relation between the radii of their circular paths and a relation between their centripetal accelerations. Try to write down some equations.
 
  • #3
Use subscripts to represent the parameters for A and B. Thus, rA, vA, and aA are the radius, velocity, and acceleration of A, respectively, and similarly for B. Now, in terms of these parameters, write the centripetal acceleration equations for A and B respectively. How is rA related to rB? How is aA related to aB? This should give you enough to solve the problem.

Chet
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that a body experiences when moving in a circular path. It is always directed towards the center of the circle and its magnitude is determined by the speed of the object and the radius of the circle.

2. How is centripetal acceleration related to a car's motion?

When a car is moving in a circular path, it experiences centripetal acceleration towards the center of the circle. This acceleration is necessary for the car to maintain its circular motion and not fly off in a straight line.

3. What factors affect the centripetal acceleration of a car?

The centripetal acceleration of a car is affected by the car's speed and the radius of the circular path it is traveling on. The greater the speed or the smaller the radius, the greater the centripetal acceleration will be.

4. How is centripetal acceleration measured?

Centripetal acceleration is measured in meters per second squared (m/s²) using the formula a = v²/r, where a is the centripetal acceleration, v is the speed of the car, and r is the radius of the circular path.

5. What are some real-life applications of centripetal acceleration in car movements?

Centripetal acceleration plays a role in various aspects of car movement, such as turning around a curve, driving on a banked road, and taking a sharp turn. It is also important in ensuring the stability and balance of a car while driving at high speeds.

Similar threads

Replies
12
Views
634
  • Introductory Physics Homework Help
2
Replies
55
Views
662
  • Introductory Physics Homework Help
Replies
4
Views
977
  • Introductory Physics Homework Help
Replies
6
Views
730
  • Introductory Physics Homework Help
Replies
28
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
681
  • Introductory Physics Homework Help
Replies
5
Views
2K
Replies
7
Views
1K
Back
Top