Calculating Centripetal Acceleration & Force in Two Cars

In summary, two cars with masses of 1080 kg and 1500 kg are traveling at the same speed of 28 m/s on a curve with a radius of 124 m. To find the centripetal acceleration and force for each car, the formula V=sqrt(rg tan theta) is used. However, since the angle of banking is not given, it is assumed to be flat. On the flat curve, the centripetal force is provided by frictional force. To find the frictional force for car A, the centripetal force must be equated. By solving for the coefficient of friction, the magnitude of the centripetal force for car A can be determined. The same process can be applied
  • #1
pookisantoki
44
0
Two cars are traveling at the same speed of 28 m/s on a curve that has a radius of 124 m. Car A has a mass of 1080 kg, and car B has a mass of 1500 kg. Find (a) the magnitude of the centripetal acceleration and (b) the magnitude of the centripetal force for Car A, (c) the magnitude of the centripetal acceleration and (d) the magnitude of the centripetal force for Car B.

I used the formula V=sqrt(rg tan theta)
for part a: v=sqrt(151*9.80 tan theta)
For part b: v=sqrt (115*9.80 tan theta)

But how would i find theta?
 
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  • #2
Why do you think the curve is banked? The centripetal acceleration doesn't depend on the banking angle anyway. What's the centripetal acceleration of an object moving at velocity v on a curve of radius r?
 
  • #3
In the problem the angle of banking is not given. So assume it as flat.
On the flat curve, the centripetal force is provided by the frictional force.
For car A, what is the frictional force? You know the centripetal force.
Equating them you can find the μs. Using this you can solve the second part.
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It always points towards the center of the circle and its magnitude can be calculated using the equation a = v^2/r, where v is the velocity of the object and r is the radius of the circle.

2. How do you calculate centripetal force?

Centripetal force is the force that keeps an object moving in a circular path. It is equal and opposite to the centripetal acceleration and can be calculated using the equation F = mv^2/r, where m is the mass of the object, v is the velocity, and r is the radius of the circle.

3. What is the difference between centripetal acceleration and tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circle, while tangential acceleration is the acceleration in the direction of the tangent to the circle. Centripetal acceleration is responsible for keeping an object moving in a circular path, while tangential acceleration can change the speed of the object.

4. Can you calculate centripetal acceleration and force for multiple objects moving in a circular path?

Yes, centripetal acceleration and force can be calculated for multiple objects moving in a circular path. Each object will have its own acceleration and force, which can be calculated using the same equations mentioned above.

5. How does the speed and radius of the circular path affect centripetal acceleration and force?

The greater the speed of the object, the greater the centripetal acceleration and force will be. This means that the object will require a stronger force to keep it moving in a circular path. Similarly, a smaller radius will result in a larger centripetal acceleration and force, as the object needs to make a sharper turn.

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