Centripetal Acceleration & Frictional Force

In summary, the maximum speed a certain light truck can go around a curve with a radius of 75.0 m is 22.6 m/s, assuming the same road conditions as the first curve with a radius of 150 m. This is found by setting the net centripetal force equal in both situations and solving for the unknown velocity.
  • #1
amaryllia
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Homework Statement


A certain light truck can go around a flat curve having a radius of 150 m with a maximum speed of 32.0 m/s. With what maximum speed can it go around a curve having a radius of 75.0 m?

Homework Equations


Fc = m(v^2/r)

Fc = net centripetal force
m = mass
v = tangenital speed
r = radius

The Attempt at a Solution



The answer I got is what is in the back of my book, but I am unsure if I took the right path to get to the answer and if my reasoning is sound. Any feedback would be greatly appreciated!

In a free body diagram of this problem the only force acting in the radial direction is the force of static friction keeping the car on the road. Although the problem does not state this directly, I'm assuming that the truck is taking the second curve of radius 75.0 m under the same road conditions as the first curve. If this is true, then the net centripetal force would be equal in both curves (the force of static friction is the same on both curves).

If Fc = m(v^2/r) and Fc is the same in both situations, then I can set m(v^2/r) of the first curve equal to the second, getting:
m(v1^2/r1) = m(v2^2/r2)
where v1 = tangenital velocity of curve 1 = 32.0 m/s
r1 = radius of curve 1 = 150 m
v2 = unknown solving for
r2 = radius of curve 2 = 75 m

I can cancel out mass, and get:
32^2/150 = v2^2/75

For a solution, I get v2 = 22.6 m/s.
 
Last edited:
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  • #2
Yes both your method and reasoning are correct.
 

1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences when it moves in a circular path. It is always directed towards the center of the circle and its magnitude depends on the speed of the object and the radius of the circle.

2. How is centripetal acceleration related to frictional force?

Frictional force is the force that opposes the motion of an object. In the case of circular motion, the centripetal acceleration is provided by the frictional force acting towards the center of the circle. This allows the object to maintain its circular path.

3. Can centripetal acceleration and frictional force be calculated?

Yes, both centripetal acceleration and frictional force can be calculated using the equations a = v^2/r and F = μN, respectively. Where v is the speed of the object, r is the radius of the circle, μ is the coefficient of friction, and N is the normal force.

4. How does the radius of the circle affect centripetal acceleration and frictional force?

The radius of the circle has a direct relationship with both centripetal acceleration and frictional force. As the radius increases, the centripetal acceleration decreases, and the frictional force required to maintain the circular motion also decreases. On the other hand, a smaller radius will result in a higher centripetal acceleration and frictional force.

5. What factors can affect the magnitude of centripetal acceleration and frictional force?

The magnitude of centripetal acceleration and frictional force can be affected by the speed of the object, the radius of the circle, and the coefficient of friction between the object and the surface it is moving on. Other factors such as the mass and shape of the object can also play a role.

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