Acceloration and tension of a pendulum

In summary, the problem involves a bowling ball attached to a ceiling by a rope and swinging back and forth as a pendulum. At one point, the ball has a speed of 4.00 m/s and the question is asking for the acceleration and tension at that instant. The acceleration can be found using geometry and the tension can be found using F = ma. The motion is circular, which explains the initial confusion.
  • #1
BoldKnight399
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A bowling ball weighing 72.0N is attached to the ceiling by a rope of length 3.78 m. the ball is pulled to one side and released; it then swings back and forth as a pendulum. As the rope swings through the vertical, the speed of the bowling abll is 4.00 m/s. What is the acceleration of the bowling ball, in magnitude and direction, at this instant?

So I was thinking that the direction would be negative and the direction would be perpendicular to the tension and the weight of the rope.
The problem is that I do not know how to get that.
Should it be that a=v^2/R like circular motion?

I also need to find the tension in the rope at this instant. I thought it would just be the opposite of the weight because the ball is not rising above itself and the tension is remaining constant. But that wasn't the right answer, so I will admit that I am totally lost and confused as to how to approach this problem now.
 
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  • #2
Hi BoldKnight399! :smile:

(try using the X2 icon just above the Reply box :wink:)

This is just another F = ma problem.

Take it step by step …

first find the acceleration, a (that's just geometry),

then (since you know the weight) use F = ma to find T. :wink:

(btw, "like circular motion"? this is circular motion! :biggrin:)
 

1. What is the formula for calculating the acceleration of a pendulum?

The formula for calculating the acceleration of a pendulum is a = -(g/L)sin(θ), where a is the acceleration, g is the acceleration due to gravity (9.8 m/s^2), L is the length of the pendulum, and θ is the angle of the pendulum with respect to the vertical.

2. How does the length of a pendulum affect its acceleration?

The length of a pendulum affects its acceleration because it is directly proportional to the gravitational force acting on the pendulum. The longer the pendulum, the greater the distance it travels and the greater the acceleration due to gravity. Therefore, a longer pendulum will have a higher acceleration compared to a shorter pendulum.

3. What is the relationship between tension and acceleration in a pendulum?

The relationship between tension and acceleration in a pendulum is that they are inversely proportional. This means that as tension increases, acceleration decreases, and vice versa. This is because tension acts as a restoring force, pulling the pendulum back to its equilibrium position and slowing down its acceleration.

4. How does the amplitude of a pendulum affect its acceleration?

The amplitude of a pendulum does not affect its acceleration. The acceleration of a pendulum is only dependent on the length, angle, and mass of the pendulum. The amplitude, which is the maximum angle the pendulum swings from its equilibrium position, only affects the period and frequency of the pendulum's motion.

5. Can the acceleration of a pendulum be greater than the acceleration due to gravity?

No, the acceleration of a pendulum cannot be greater than the acceleration due to gravity. The acceleration of a pendulum is always equal to or less than the acceleration due to gravity, depending on the length and angle of the pendulum. This is because the acceleration due to gravity is the maximum acceleration that a pendulum can achieve as it swings back and forth.

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