Solving for Slowest Speed of a Ball: 2.25m Radius

In summary, the conversation discusses a problem involving a ball with a radius of 2.25 m spinning in a circular path. The question is what is the slowest speed the ball needs to have at the bottom in order to make it around to the top of the path. The conversation includes a request for clarification of the problem statement and a suggestion to draw a free body diagram and use Newton's second law to solve the problem. The final response confirms the understanding of the problem and provides the correct formula for solving it.
  • #1
liz777
19
0

Homework Statement


A ball has a radius of 2.25 m. What is the slowest speed of the ball at the bottom which will just make it around at the top of the path?

The Attempt at a Solution



I don't even know where to start with this problem. I don't understand it. Any help would be greatly appreciated!
 
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  • #2
liz777 said:
I don't even know where to start with this problem. I don't understand it.

Neither do I, because you didn't type in the entire problem statement. I'm guessing that the ball is tethered to a rope of radius 2.25 m, but that's just a guess. Please type in the problem statement exactly as it appears on your assignment.
 
  • #3
oh sorry...here it is:

When one spins a ball in a circular path which has a radius of 2.25 m, what is the slowest speed of the ball at the bottom which will just make it around at the top of the path?
 
  • #4
You should begin by drawing a free body diagram of the ball at the top of its path. Then write down Newton's second law for the ball at that point. That's how you start all dynamics problems at this level.
 
  • #5
ok, I drew a diagram and I think I understand. Gravity pulls down on the ball, which is the acceleration so:
v^2=gr
=(9.8)(2.25)

Is this correct?
 
  • #6
Right, just remember to take the square root. You found [itex]v^2[/itex], not [itex]v[/itex].
 
  • #7
ok, thank you! :) I understand it.
 

1. What is the formula for calculating the slowest speed of a ball with a 2.25m radius?

The formula for calculating the slowest speed of a ball with a 2.25m radius is v = √(g*r), where v is the velocity, g is the acceleration due to gravity (9.8 m/s²), and r is the radius of the ball (2.25m).

2. How do you determine the slowest speed of a ball in a real-world scenario?

In a real-world scenario, the slowest speed of a ball can be determined by using a motion sensor or a stopwatch to measure the time it takes for the ball to travel a known distance. This time can then be used in the formula v = √(g*r) to calculate the slowest speed.

3. Can the slowest speed of a ball be faster than the initial speed?

No, the slowest speed of a ball cannot be faster than the initial speed. The initial speed is the speed at which the ball is released or thrown, and the slowest speed is the minimum speed the ball will reach due to the effects of gravity and air resistance.

4. How does air resistance affect the slowest speed of a ball?

Air resistance, also known as drag, can decrease the slowest speed of a ball. As the ball moves through the air, it experiences a force in the opposite direction of its motion, which slows it down. This means that the slowest speed of a ball in a real-world scenario may be slightly lower than the calculated value.

5. What are some real-life applications of calculating the slowest speed of a ball?

Calculating the slowest speed of a ball is important in various sports and activities such as baseball, golf, and bowling. It can also be useful in engineering and design to ensure the safety and functionality of objects such as roller coasters, cars, and airplanes.

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