# Tangential and Centripetal Acceleration

• kwenz21
In summary, the discussion is about a problem involving a bike traveling up and over a hill with a radius of 10 meters and a picture showing an angle of 60 degrees between points A and B. The problem asks to determine the average tangential acceleration while slowing down, the centripetal acceleration, and the net acceleration and its direction. The equations used are a(centripetal)=v^2/r and the attempt at a solution involved finding an average acceleration of -2.5 m/s^2 and being unable to determine the tangential acceleration without more information. Further details and clarification are needed, such as whether the cyclist is applying force to the pedals and the location of points A and B in relation to the hill.
kwenz21

## Homework Statement

A bike is travel up and over a hill with a radius at the top of the hill of 10 meters. The bike is traveling at 10 m/s at position A and 5 m/s at position. (and the problem comes with a picture showing an angle of 60* between point A and B.

a. Determine the average tangential acceleration while slowing down
b. Determine the centripetal acceleration
c. Determine the net acceleration and its direction

## Homework Equations

I used a(centripetal)=v^2/r and I was unsure of how to get tangential

## The Attempt at a Solution

I evantually came out with a being equal to -2.5 m/s^2 (-5^2/10) and I was unable to get tangential just putting down my best guess which made it impossible for me to get a and c correct

kwenz21 said:

## Homework Statement

A bike is travel up and over a hill with a radius at the top of the hill of 10 meters. The bike is traveling at 10 m/s at position A and 5 m/s at position. (and the problem comes with a picture showing an angle of 60* between point A and B.

a. Determine the average tangential acceleration while slowing down
b. Determine the centripetal acceleration
c. Determine the net acceleration and its direction

## Homework Equations

I used a(centripetal)=v^2/r and I was unsure of how to get tangential

## The Attempt at a Solution

I evantually came out with a being equal to -2.5 m/s^2 (-5^2/10) and I was unable to get tangential just putting down my best guess which made it impossible for me to get a and c correct
Is the cyclist applying force to the pedals as he goes up the hill? In other words, is the cyclist adding energy to the bike or is the bike coasting up the hill?

I think you will have to provide the diagram or provide some more details of where A and B are in terms of horizontal and vertical distance from the top and base of the hill.

AM

This is the exact problem that was given to me. Sorry if some parts are hard to see the only relevant things I can think of that are in the picture and not the descriptionis that the radius of the circle is 10m and the angle between A and B is 60*

#### Attachments

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Average acceleration means that constant acceleration which would result in the same change of velocity and distance traveled in the same time. Assuming constant tangential acceleration and the path taken as pi/3 R, and knowing the initial and final speeds, how do you determine the acceleration?

As for the centripetal acceleration, the text does not specify if it is at A or B or at the maximum height. ehild

.

Thank you for providing your attempt at a solution. It seems like you are on the right track with using the equation a(centripetal) = v^2/r to solve for the centripetal acceleration. However, in order to find the tangential acceleration, you will need to use the equation a(tangential) = (vf - vi)/t, where vf is the final velocity, vi is the initial velocity, and t is the time.

To solve for a(tangential), you will need to first determine the time it takes for the bike to travel from position A to position B. This can be found using the equation vf = vi + at, where vf is the final velocity (5 m/s), vi is the initial velocity (10 m/s), and a is the unknown acceleration. Rearranging the equation, we get t = (vf - vi)/a.

Substituting in the known values, we get t = (5 - 10)/a = -5/a. Now, we can plug in this value of t into the equation a(tangential) = (vf - vi)/t to solve for a(tangential). This gives us a(tangential) = (5 - 10)/(-5/a) = -a. Therefore, the average tangential acceleration while slowing down is also equal to -a.

To find the net acceleration, we can use the Pythagorean theorem to combine the tangential and centripetal accelerations. This gives us a(net) = √(a(tangential)^2 + a(centripetal)^2). We can also find the direction of the net acceleration by using the equation tanθ = a(centripetal)/a(tangential), where θ is the angle between the net acceleration and the tangential acceleration.

I hope this helps and clarifies any confusion you had. Keep up the good work!

## 1. What is tangential acceleration and how is it calculated?

Tangential acceleration is the acceleration along the tangent of a circular path. It is calculated using the formula a = v^2/r, where v is the velocity and r is the radius of the circular path.

## 2. What is centripetal acceleration and how is it different from tangential acceleration?

Centripetal acceleration is the acceleration towards the center of a circular path. It is always perpendicular to the tangential acceleration. It is calculated using the formula a = v^2/r, where v is the velocity and r is the radius of the circular path. Unlike tangential acceleration, which is always present in a circular motion, centripetal acceleration only exists when there is a change in direction or speed of the object in circular motion.

## 3. Can an object have both tangential and centripetal acceleration at the same time?

Yes, an object can have both tangential and centripetal acceleration at the same time. This is because tangential acceleration is the component of the object's overall acceleration that is in the direction of its motion, while centripetal acceleration is the component that is perpendicular to its motion.

## 4. How does tangential and centripetal acceleration affect an object in circular motion?

Tangential acceleration affects the speed of the object in circular motion, while centripetal acceleration affects the direction of the object's motion. Together, they determine the overall acceleration of the object in circular motion.

## 5. Can tangential and centripetal acceleration be negative?

Yes, both tangential and centripetal acceleration can be negative. A negative tangential acceleration would indicate that the object is slowing down, while a negative centripetal acceleration would indicate that the object is moving in the opposite direction of the center of the circular path.

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