Conservation of Energy pinball problem

In summary, the ball launcher in a pinball machine has a spring with a force constant of 1.10 N/cm and the surface on which the ball moves is inclined 10.0° with respect to the horizontal. When the spring is initially compressed 5.00 cm, the launching speed of a 0.100 kg ball is 1.61 m/s when the plunger is released. The presence of friction and the mass of the plunger are negligible in this calculation.
  • #1
SamTsui86
31
0
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 5.00 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.

p5-71.gif


so here's what i did

Ei = Ef, so

1/2kx^2 = mgsin@x + 1/2 mv^2

I got .377 m/s for the answer, but the real answer is 1.61 m/s

Plz tell me what i did wrong.

Thank You
 
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  • #2
Apparently you did the arithmetic wrong. I used your formula and got 1.61 m/s (actually, I got 161 but then realized I was still in cm/s !)
 
  • #3
ohhh, i made the same mistake too, except convert on of them to m but not all. Thank You
 

1. What is the Conservation of Energy pinball problem?

The Conservation of Energy pinball problem is a physics problem that involves a ball rolling down a ramp and colliding with a pinball at the bottom. The question is whether the total energy of the system (ball and pinball) remains the same before and after the collision.

2. Why is the Conservation of Energy important in this pinball problem?

The Conservation of Energy is important in this pinball problem because it is a fundamental principle in physics. It states that energy cannot be created or destroyed, only transferred or transformed. This means that the total energy of the system should be the same before and after the collision, unless there are external forces acting on the system.

3. How does the potential energy of the ball change in this problem?

In this problem, the potential energy of the ball decreases as it rolls down the ramp due to the force of gravity. At the bottom of the ramp, the potential energy is converted into kinetic energy as the ball gains speed. During the collision with the pinball, some of the kinetic energy is transferred to the pinball, resulting in a decrease in the ball's kinetic energy and an increase in the pinball's kinetic energy.

4. What is the role of friction in the Conservation of Energy pinball problem?

Friction is a non-conservative force that can affect the total energy of the system. In this problem, friction between the ball and the ramp can cause some energy to be lost as heat, leading to a decrease in the total energy of the system. This means that the final kinetic energy of the system may be less than the initial potential energy of the ball.

5. How does the mass of the pinball affect the Conservation of Energy in this problem?

The mass of the pinball does not directly affect the Conservation of Energy in this problem. It only affects the amount of kinetic energy the pinball gains during the collision. However, the total mass of the system does play a role in the Conservation of Energy, as the total energy should remain the same regardless of the mass of the objects involved.

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