# Solve Centripetal Motion Problem: Find Tension & Acceleration

• rickylin89
In summary: I don't understand how to apply Newton's second law.I think you need to find the net force acting on the object, and then use the law to find the acceleration.For example, if there is a net force of -10 N acting on the object, then the acceleration would be 10 m/s/s.I don't understand how to find the net force.I think you need to find the total force acting on the object, and then use the law to find the acceleration.For example, if there is a total force of 10 N acting on the object, then the acceleration would be 10 m/s/s.In summary, Rickylin89 has a problem trying to figure out how to calculate the acceleration of
rickylin89
I have a problem that I've tried to figure out, but I can't figure it out.

Here it is:

You whirl a ball of mass 0.40 kg on a string of length 0.90 m. At the point shown the angle of the string from the vertical is 30 degrees and the ball has a speed of 3.5 m/s.

a) Make a free body diagram of the ball.
b) Find the tension in the string.
c) What is the acceleration of the ball, tangential and radial components?
c) Now consider the ball at the top of the circle. What is the smallest speed of the ball so that the ball continues in a circle?

Any help with this problem would be greatly appreciated!

Last edited:
I have a homework problem that I've tried to figure out, but I can't figure it out.

Here it is:

You whirl a ball of mass 0.40 kg on a string of length 0.90 m. At the point shown the angle of the string from the vertical is 30 degrees and the ball has a speed of 3.5 m/s.

a) Make a free body diagram of the ball.
b) Find the tension in the string.
c) What is the acceleration of the ball, tangential and radial components?
c) Now consider the ball at the top of the circle. What is the smallest speed of the ball so that the ball continues in a circle?

Any help with this problem would be greatly appreciated!

Hi rickylin89!

Show us what you've tried, and where you're stuck, and then we'll know how to help.

Honestly, I really don't know how to start this problem. Any help would b great.

Draw a free body diagram and write the equations of motion. If you are familiar with them, us the polar coordinate form for the equations of motion; it will make things easiest.

I'm not sure if I have the right free body diagram. I figured there was a down force of gravity, an up force of net force, and then I don't know what other forces there are.

Where does this "up force" come from? The only forces you can include have to come from somewhere!

What direction is the force in the string?

I think there is a tension that is 60 degrees to the left of the down force of mg. Is that righ?

What matters is that the tension in the strings is ALONG the strong.

I don't really understand what you mean.

The tension is along the string, but I was referring to the free body diagram and the fact that the tension is mgsin(60). Is that right?

No, that is really not correct. Just call the tension T for right now, but recognize that it acts along the string. The apply Newton's second law, with the proper acceleration of the mass and the correct force sums along the string and perpendicular to the string.

## 1. What is centripetal motion and how is it different from linear motion?

Centripetal motion is the circular motion of an object around a fixed point. It is different from linear motion because the direction of the object's velocity is constantly changing, as it is always directed towards the center of the circle.

## 2. How do you calculate the tension in a centripetal motion problem?

The tension in a centripetal motion problem can be calculated using the formula T = mv²/r, where T is the tension, m is the mass of the object, v is the velocity, and r is the radius of the circle.

## 3. What is the relationship between tension and acceleration in a centripetal motion problem?

The tension and acceleration in a centripetal motion problem are directly proportional. This means that as the tension increases, the acceleration also increases, and vice versa. This is because the tension is responsible for providing the centripetal force that keeps the object moving in a circular path.

## 4. Can you solve a centripetal motion problem with only the tension and mass given?

Yes, you can solve a centripetal motion problem with only the tension and mass given. You can use the formula a = T/m to calculate the acceleration, and then use this value to solve for other unknowns, such as the velocity or radius.

## 5. What are some real-life examples of centripetal motion?

Some common examples of centripetal motion include the rotation of a car's tires while turning, the motion of a satellite orbiting the Earth, and the swinging of a pendulum. Roller coasters and carnival rides also often involve centripetal motion.

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