Energy and Simple Harmonic Motion

In summary, a ball is shot in a pinball machine by a compressed spring and slides to a higher point. To calculate its speed at that point, use the equation for conservation of energy instead of the one provided. The ball's initial spring potential energy transforms into kinetic energy and gravitational potential energy as it moves to point B. Set up the equation and solve for the speed.
  • #1
shawonna23
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0
In preparation for shooting a ball in a pinball machine, a spring (k = 675 N/m) is compressed by 0.0690 m relative to its unstrained length. The ball (m = 0.0540 kg) is at rest against the spring at point A. When the spring is released, the ball slides (without rolling) to point B, which is 0.300 m higher than point A. How fast is the ball moving at B?


I used this equation: v final=square root of k/m(x initial^2 - x final^2)
but I keep getting the wrong answer. Am I using the wrong equation? Can someone help me?
 
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  • #2
Instead of using that equation, think in terms of conservation of energy: Initially, the ball has only spring potential energy ([itex]1/2 k x^2[/itex]), which gets transformed into kinetic energy plus gravitational potential energy as it moves to position B. Set up that equation and solve for the speed.
 
  • #3


It seems like you are using the correct equation, but there may be an error in your calculations. Let's break down the problem and go through it step by step to see if we can identify the issue.

First, we need to find the potential energy stored in the spring when it is compressed by 0.0690 m. We can use the equation for potential energy in a spring, U = 1/2*k*x^2, where k is the spring constant and x is the distance the spring is compressed. Plugging in the values given, we get U = 1/2 * 675 N/m * (0.0690 m)^2 = 16.35 J.

Next, we can use the conservation of energy principle to find the kinetic energy of the ball at point B. At point A, the ball has zero kinetic energy since it is at rest. At point B, all of the potential energy stored in the spring is converted into kinetic energy. So, we can set the potential energy at point A equal to the kinetic energy at point B. This gives us the equation 16.35 J = 1/2 * m * v^2, where v is the velocity of the ball at point B. Plugging in the given mass of the ball, we get 16.35 J = 1/2 * 0.0540 kg * v^2. Solving for v, we get v = 7.26 m/s.

So, the ball will be moving at a speed of 7.26 m/s at point B. Make sure to double check your calculations and units to ensure you get the correct answer. It may also be helpful to draw a diagram and label all the given values to keep track of them. Keep practicing and you will become more confident in solving problems like this!
 

Related to Energy and Simple Harmonic Motion

1. What is energy and how is it related to simple harmonic motion?

Energy is the ability to do work. In simple harmonic motion, energy is constantly being exchanged between potential energy (stored energy) and kinetic energy (energy of motion). As the object oscillates, its potential energy is highest at the turning points and its kinetic energy is highest at the equilibrium point.

2. How is the potential energy of a simple harmonic oscillator calculated?

The potential energy of a simple harmonic oscillator is calculated using the equation PE = 1/2kx^2, where k is the spring constant and x is the displacement from equilibrium.

3. What is the period of a simple harmonic oscillator and how is it related to energy?

The period of a simple harmonic oscillator is the time it takes for one complete oscillation. It is related to energy through the equation T = 2π√(m/k), where m is the mass of the object and k is the spring constant. As the energy of the oscillator increases, the period decreases.

4. How does the amplitude of a simple harmonic oscillator affect its energy?

The amplitude of a simple harmonic oscillator is the maximum displacement from equilibrium. As the amplitude increases, so does the energy of the oscillator. This is because the potential energy is directly proportional to the square of the amplitude.

5. What factors affect the frequency of a simple harmonic oscillator?

The frequency of a simple harmonic oscillator is affected by the mass of the object, the spring constant, and the amplitude. As the mass or spring constant increases, the frequency decreases. As the amplitude increases, the frequency also increases.

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