# Centripetal Acceleration and Force

In summary, the conversation discusses the calculation of the centripetal acceleration and force for a small truck riding in a circle with a radius of 40m at a constant speed of 70m/s. The calculated values for both parameters seem high, but this is expected due to the nature of circular motion and the need for a strong centripetal force to maintain the circular path.

## Homework Statement

A small truck of mass 1600kg rides in a circle of which has a radius of 40m at a constant speed of 70m/s

Calculate:
(a) its centripetal acceleration
(b)the centripetal force acting.

## Homework Equations

$a_{centripetal} = {v^2 \over r} \\ F_{centripetal} = {mv^2 \over r}$

## The Attempt at a Solution

I think I got the correct answers its just the figures seem absurdly high, so can someone check my understanding please?

So for part a
$a_{centripetal} = {70^2 \over 40} \\ a_{centripetal} = 122.5 m/s^2$

And part b
$F_{centripetal} = \frac{1600 \times 70^2}{40} \\ F_{centripetal} = \frac{7840000}{40} \\ F_{centripetal} = 196kN$

The figures just seem to high to me, we only had one lesson on this so I may have taken down something wrong or might have misunderstood the question.

Looks fine to me.

Doc Al said:
Looks fine to me.

OK, thanks :)

The figures just seem to high to me …

looks ok to me, too

imagine you had to pull on a rope to keep it in a circle …

wouldn't you expect to pull really hard?

Any help would be appreciated.

Your calculations for both parts are correct. The figures may seem high because of the high speed and mass of the truck. Centripetal acceleration and force are directly proportional to the square of the velocity, so as the speed increases, so does the acceleration and force. Additionally, the radius of the circle is relatively small, which also contributes to the high values.

## 1. What is centripetal acceleration?

Centripetal acceleration is the acceleration that an object experiences when moving in a circular path. It is always directed towards the center of the circle and is caused by a force called centripetal force.

## 2. How is centripetal acceleration calculated?

The formula for calculating centripetal acceleration is a = v^2/r, where "a" is the acceleration, "v" is the velocity, and "r" is the radius of the circular path. This formula applies to objects moving at a constant speed in a circular motion.

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

Centripetal acceleration is the acceleration towards the center of the circle, while tangential acceleration is the acceleration along the tangent line of the circle. Centripetal acceleration is always present in circular motion, but tangential acceleration only exists when there is a change in the object's speed.

## 4. What is centripetal force?

Centripetal force is the force that is responsible for keeping an object moving in a circular path. It is always directed towards the center of the circle and is equal to the mass of the object multiplied by its centripetal acceleration.

## 5. How does centripetal acceleration affect the motion of objects?

Centripetal acceleration causes a change in the direction of an object's motion, but not its speed. This means that an object moving in a circular path at a constant speed is still accelerating due to the constant change in direction. Centripetal acceleration also increases as the object's speed or the radius of the circular path increases.

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