How Do You Calculate the Launch Speed of a Ball in a Pinball Machine?

[Touchme]

The ball launcher in a pinball machine has a spring with a force constant of 1.10 N/cm (Fig. P5.71). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.00 cm, find the launching speed of a 0.100 kg ball when the plunger is released. Friction and the mass of the plunger are negligible.

I converted all the cm to m (0.011 N/m and 0.04m). I apply the Conservation of mechanical energy. Initial KE and PE is 0. I also set final PE as 0 and solved for final velocity. So I tried (1/2)(k)(x^2) = (1/2)mv^2
however it is incorrect. I also try taking the final velocity and dividing it by cos 10. Wrong and not sure why I did that . What am I doing wrong?

 

[OlderDan]

The ball launcher in a pinball machine has a spring with a force constant of 1.10 N/cm (Fig. P5.71). The surface on which the ball moves is inclined 10.0° with respect to the horizontal. If the spring is initially compressed 4.00 cm, find the launching speed of a 0.100 kg ball when the plunger is released. Friction and the mass of the plunger are negligible.

I converted all the cm to m (0.011 N/m and 0.04m). I apply the Conservation of mechanical energy. Initial KE and PE is 0. I also set final PE as 0 and solved for final velocity. So I tried (1/2)(k)(x^2) = (1/2)mv^2
however it is incorrect. I also try taking the final velocity and dividing it by cos 10. Wrong and not sure why I did that . What am I doing wrong?

The final PE is not zero. There are two sources of PE important to this problem. Furthermore, your statement that the initial PE is zero is contradicted by your equation

(1/2)(k)(x^2) = (1/2)mv^2

What this equation implies is that the initial potential energy of the spring is converted to kinetic energy of the ball. That's good as far as it goes, but it leaves out that other potential energy consideration.

 

[Touchme]

If the final PE is not zero, the problem is how to determine the PE if the only distance given is the displacement from equilibrium. Furthermore, the height is unknown.

 

[OlderDan]

If the final PE is not zero, the problem is how to determine the PE if the only distance given is the displacement from equilibrium. Furthermore, the height is unknown.

The plunger is on an incline. You know how far the plunger moves. When the plunger is released the spring does work on the ball equal to its stored energy. Some of that work increases the gravitiaonal potential energy of the ball because it goes up the incline. The rest of the work is the kinetic energy of the ball

 

[Touchme]

Hmm... I think I understand now. The plunger moves 4cm because that is the distance traveled when the plunger is launched. Also the 4cm is the distance moved up an incline, so I have to find the h value (4sin10). Am I on the right track, if so then I think I can solve this?

 

[OlderDan]

Hmm... I think I understand now. The plunger moves 4cm because that is the distance traveled when the plunger is launched. Also the 4cm is the distance moved up an incline, so I have to find the h value (4sin10). Am I on the right track, if so then I think I can solve this?

Yes. That is what you need.