Energy of Motion: 2.4kg-mass w/ 7.0cm amp & 5.0Hz freq

In summary, the 2.4kg mass attached to a spring with an amplitude of 7.0cm and a frequency of 5.0Hz has an energy of motion of approximately 580J. This can be calculated using the formula E = 1/2*k*x^2, where k is the spring constant and x is the amplitude. However, if the maximum speed of the bob is known, the formula E = 1/2*m*v^2 can also be used to calculate the energy.
  • #1
nlkush
7
0

Homework Statement


A 2.4kg- mass attached to a spring oscillates with an amplitude of 7.0cm and a frequency of 5.0Hz .
What is its energy of motion?
Express your answer using two significant figures.
in J.

Homework Equations





The Attempt at a Solution

 
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  • #2
people are going to ask you to give it a shot be for they help. Let's start with what equations should you use>
 
  • #3
You have two energy formulas that apply:
E = 1/2*k*x^2 for when the spring is stretched but the bob is not moving.
E = 1/2*m*v^2 when the object is moving but the spring is not stretched.
Looks like the first one will be easier to work out!
 
  • #4
ok i have my T which is 0.2s
omega is 31.4
k is 2366.3
and amplitude is 7
eqn to be used is E=1\2kA(squared) i believe but i cannot get the correct answer doing so
 
  • #5
I haven't seen E = 1/2*k*x^2 written with an A instead of an x.
The x means "extension" or how much the spring is stretched.
Or compressed.
That just means the 7 cm, I think.

As the spring oscillates, this energy is repeatedly converted back and forth between spring energy and kinetic energy. If you knew the maximum speed of the bob, you could use E = 1/2mv^2 and get the same answer. Or you could set 1/2*k*x^2 at maximum extension equal to 1/2mv^2 at maximum speed and solve for the speed.
 
  • #6
i see, i still cannot get the right answer i don't no waht I am doing wrong
 
  • #7
my answers come to 580 or 5.8*10^5
and it comes up wrong
 

1. What is the energy of motion?

The energy of motion, also known as kinetic energy, is the energy an object possesses due to its motion. It is dependent on the mass and velocity of an object.

2. How is the energy of motion calculated?

The energy of motion is calculated using the equation E = 1/2mv^2, where E is the energy in joules, m is the mass in kilograms, and v is the velocity in meters per second.

3. What is the mass and amplitude in this scenario?

In this scenario, the mass is 2.4kg and the amplitude is 7.0cm. The mass is the amount of matter in an object, while the amplitude is the maximum displacement from equilibrium in a periodic motion.

4. How does frequency affect the energy of motion?

The frequency, which is the number of cycles or oscillations per second, is directly proportional to the energy of motion. This means that as the frequency increases, the energy of motion also increases.

5. Can the energy of motion be converted into other forms of energy?

Yes, the energy of motion can be converted into other forms of energy, such as thermal energy or potential energy. This is known as the law of conservation of energy, which states that energy cannot be created or destroyed, but can only be converted from one form to another.

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