Conservation of Energy Ball Problem

[clairez93]

Homework Statement

A 2.00-kg ball is attached to the bottom end of a length of 10-lb (44.5-N) fishing line. The top end of the fishing line is held stationary. The ball is released from rest while the line is taut and horizontal ($$\theta$$) = 90.0 degrees). At what angle $$\theta$$ (measured from the vertical) will the fishing line break?

Homework Equations

Conservation of Energy:
K_i + U_i = K_f + U_f

The Attempt at a Solution

I'm pretty sure that I have to start with the conservation of energy equation, however, I am not quite sure that I have enough numbers to put into solve for anything. Also, I have no idea what circumstances would cause the fishing line to break. I'm just clueless as to where to begin here.

 

[LowlyPion]

Homework Statement

A 2.00-kg ball is attached to the bottom end of a length of 10-lb (44.5-N) fishing line. The top end of the fishing line is held stationary. The ball is released from rest while the line is taut and horizontal ($$\theta$$) = 90.0 degrees). At what angle $$\theta$$ (measured from the vertical) will the fishing line break?

Homework Equations

Conservation of Energy:
K_i + U_i = K_f + U_f

The Attempt at a Solution

I'm pretty sure that I have to start with the conservation of energy equation, however, I am not quite sure that I have enough numbers to put into solve for anything. Also, I have no idea what circumstances would cause the fishing line to break. I'm just clueless as to where to begin here.

At what force will the line break? 10 lb test line breaks at ...44.5N? That's what it looks like.

So ... what will the force on the line be?

Doesn't the change in potential energy = kinetic? Might that have something to do with the velocity?

Won't there also be a component of gravity acting on the weight?

 

[baba89]

As a scientist, it is important to first identify all the given information and variables in the problem. In this case, we are given the mass of the ball (2.00 kg), the tension in the fishing line (44.5 N), and the initial angle of the fishing line (90 degrees). We are also asked to find the angle at which the fishing line will break.

To solve this problem, we can use the principle of conservation of energy. This principle states that energy cannot be created or destroyed, only transferred from one form to another. In this case, the potential energy of the ball at the top of the fishing line will be converted into kinetic energy as it falls, until the fishing line breaks.

We can use the conservation of energy equation, Ki + Ui = Kf + Uf, where Ki is the initial kinetic energy, Ui is the initial potential energy, Kf is the final kinetic energy, and Uf is the final potential energy.

At the top of the fishing line, the ball has no kinetic energy and only potential energy given by the equation Ui = mgh, where m is the mass of the ball, g is the acceleration due to gravity, and h is the height of the ball above the ground.

As the ball falls, its potential energy is converted into kinetic energy, given by the equation Kf = (1/2)mv^2, where m is the mass of the ball and v is its final velocity.

Since we are looking for the angle at which the fishing line will break, we can set the final potential energy to zero, as all of the ball's potential energy will be converted into kinetic energy before the line breaks. This gives us the equation Ki = Kf, or mgh = (1/2)mv^2.

We can then solve for the final velocity, v, using the equation v = sqrt(2gh). Once we have the final velocity, we can use trigonometry to find the angle at which the fishing line will break. This angle can be calculated using the equation tan(theta) = v/vx, where vx is the horizontal component of the ball's velocity.

In conclusion, by applying the principle of conservation of energy and using the given information and equations, we can determine the angle at which the fishing line will break. This problem highlights the importance of understanding and applying fundamental scientific principles in solving real-world problems.