Tension and speed of bowling ball pendulum passing the equilibrium position

In summary, for part a, conservation of energy was used to determine the velocity of the ball: v = sqrt(2*g*L(1-cos(θ))). For part b, the incorrect assumption that T = mg at the equilibrium point was made, but the correct answer is T = mg*(3-2*cos(theta)). A homemade sketch of the problem was provided for reference.
  • #1
snormanlol
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Homework Statement
A bowlingball with mass m is hanging on a roof with a wire of length L. The ball is pushed out of equilibrium so that the ball makes an angle θ with the vertical. After letting go it makes a pendulum move. a) Determine the speed of the bowlingball when reaching the equilibrium position. b)Determine the tension of the wire in fuction of L,M and θ.
Relevant Equations
mgh=1/2*m*v^2
F=m*a
For part a I used conservation of energy.
-m*g*cos(θ)*L+1/2*m*0^2=-m*g*L +1/2*m*v^2 => v = sqrt(2*g*L(1-cos(θ )).
b) For b I was think that T = mg in the equilibrium point but that doesn't invole θ in the answer. So that's why I tought that T*cos(θ ) = mg. So that the tension is mg/cos(θ). But this isn't correct. The answer has to be T = mg*(3-2*cos(theta)).
Thanks for the help in advance. And I apologize for my bad english it isn't my native language.
And here is a homemade sketch of the problem.
 

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  • #2
Hello snorman,
snormanlol said:
think that T = mg in the equilibrium point
That would be correct if the ball were not moving. But it is, and the kind of trajectory it describes should help you think of what else ##T## has to do except keeping the ball from accelerating downwards :smile:
 
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  • #3
Hi bVU,
Thanks for the tip. arad= v^2/L. So that a = 2*g*(1-cos(theta)).
T - mg = 2*m*g*(1-cos(theta)) => T =mg(3-2*cos(theta))
 
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Related to Tension and speed of bowling ball pendulum passing the equilibrium position

1. What factors affect the tension and speed of a bowling ball pendulum?

The tension and speed of a bowling ball pendulum are affected by several factors, including the length of the string, the mass of the ball, and the angle at which the ball is released. The gravitational force acting on the ball and air resistance can also impact the tension and speed of the pendulum.

2. How does the length of the string affect the tension and speed of a bowling ball pendulum?

The length of the string has a direct impact on the tension and speed of the pendulum. A longer string will result in a greater tension and slower speed, while a shorter string will have less tension and a faster speed. This is because a longer string increases the distance the ball has to travel, which requires more energy to overcome the force of gravity.

3. What happens to the tension and speed of a bowling ball pendulum as it passes the equilibrium position?

As the pendulum passes the equilibrium position, the tension and speed will decrease. This is because the ball is moving against the force of gravity and air resistance, causing it to slow down. The tension in the string will also decrease as the ball moves away from the equilibrium position.

4. How does the mass of the bowling ball affect the tension and speed of the pendulum?

The mass of the ball has a significant impact on the tension and speed of the pendulum. A heavier ball will require more force to overcome the force of gravity, resulting in a higher tension and slower speed. On the other hand, a lighter ball will have less tension and a faster speed due to the lower force needed to move against gravity.

5. Does air resistance play a role in the tension and speed of a bowling ball pendulum?

Yes, air resistance does play a role in the tension and speed of the pendulum. As the ball swings, it will encounter air resistance, which will slow it down. This resistance will increase as the speed of the pendulum increases and can impact the overall tension and speed of the pendulum.

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