Potential Energy converted to kinetic energy

In summary, a 500 gram projectile is loaded into a spring gun, and the question is asked about the potential and kinetic energy at a specific position and time. Using the formula for kinetic energy and converting units, it is determined that the kinetic energy is 3618 grams/cm squared/seconds squared. However, the question of converting to meters and kilograms is raised, and it is suggested to do so before multiplying. It is also noted that if the spring has no mass, then no potential energy is converted to kinetic energy within the spring itself.
  • #1
kelly0107
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Homework Statement



A spring gun is loaded with a 500 gram projectile (position is given in centimeters and time is given in seconds) The spring is massless and therefore has no kinetic energy. How much potential energy is converted to kinetic energy when the ball is at -4 cm.

Velocity=2.69 cm/s
Time=.72 seconds



Homework Equations



K=1/2 mv squared

The Attempt at a Solution



1/2 (500g)(7.236 cm squared/seconds squared)

3618 grams/cm squared/seconds squared

Now I don't know how to set up the conversion to meters and kilograms. Can someone please help?

The other question I have is... How much potential energy is converted to kinetic energy in the spring gun? Would the answer be zero because the spring is massless?
 
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  • #2
I think it would be much easier to convert to kilograms and meters before you multiplied everything out. That way your answer for the kinetic energy would already come out in Joules. This way, you only need to remember the conversions for the basic units and all other, more complicated units will already be converted once you get to them!:smile:

If the spring is taken to have 0 mass, then assume that it has no kinetic energy. Therefore, none of the potential energy is lost to the spring itself. (Obviously, in a real spring with mass, energy is lost to the spring.)
 
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  • #3




I would like to clarify a few points before providing a response. First, it is important to note that the units for potential energy and kinetic energy are different. Potential energy is typically measured in joules (J) while kinetic energy is measured in joules per kilogram (J/kg). Therefore, in order to properly calculate the conversion of potential energy to kinetic energy, we must convert all units to the appropriate forms.

To convert the given mass of 500 grams to kilograms, we divide by 1000, giving us 0.5 kg. Similarly, to convert the given velocity of 2.69 cm/s to m/s, we divide by 100, giving us 0.0269 m/s.

Now, to calculate the kinetic energy of the projectile at -4 cm, we can use the formula K=1/2 mv^2, where m is the mass in kilograms and v is the velocity in m/s. Plugging in the values, we get:

K=1/2 (0.5 kg)(0.0269 m/s)^2 = 0.00036 J

Therefore, at -4 cm, the potential energy is converted to 0.00036 joules of kinetic energy.

As for the second question, regarding the conversion of potential energy to kinetic energy in the spring gun, it is important to note that even though the spring itself may have no mass, it still stores potential energy when it is compressed. When the spring is released, this potential energy is converted into kinetic energy, which is then transferred to the projectile. Therefore, in this scenario, the answer would not be zero, but rather the value calculated above (0.00036 J).
 

1. What is potential energy and kinetic energy?

Potential energy is the energy an object has due to its position or state. Kinetic energy is the energy an object has due to its motion.

2. How is potential energy converted to kinetic energy?

Potential energy can be converted to kinetic energy when an object's position or state changes, causing it to start moving. This can happen through the force of gravity, such as when a ball is dropped from a height, or through other external forces acting on the object.

3. What is the relationship between potential energy and kinetic energy?

Potential energy and kinetic energy are two forms of energy that are constantly changing and interrelated. As potential energy decreases, kinetic energy increases, and vice versa. The total energy of a system remains constant, but the form of energy may change.

4. What factors affect the conversion of potential energy to kinetic energy?

The amount of potential energy an object has depends on its mass, height, and the force acting on it. The conversion of potential energy to kinetic energy also depends on external factors such as friction and air resistance.

5. Can potential energy be converted to kinetic energy without losing any energy?

In theory, yes. In practice, there will always be some loss of energy due to factors like friction and air resistance. However, this loss can be minimized through efficient design and use of energy-saving techniques.

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