Calculating Maximum Speed of 2kg Block on a Spring

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In summary, the 2 kg block attached to a spring with a spring constant of 50 N/m will reach its maximum speed of 4.0 meters per second at the equilibrium point, where it has the greatest force of gravity acting on it. This force is constant throughout and can be calculated using the equation g = -GM/r^2, where G is the gravitational constant and r is the distance from the center of the Earth. The maximum speed can also be understood through energy considerations without any calculations.
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JOJOKOY
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A 2 kg block is attached to the bottom of a spring that has spring constant of 50 N/m and block is at first at equilibrium point where it will hang motionless if undisturbed. Where will it be when it reaches its maximum speed of 4.0 meters per second?

I thought it would be the equilibrium point because that is when it has the greatest force of gravity acting on it.
 
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The force of gravity is constant through out. Start with the position equation for simple harmonic motion.
 
  • #3
The gravitational field is calculated from g = -GM/r^2 where the negative sign indicates that the field is toward mass M, which in this case would be the mass of the Earth. G is the gravitational constant and r is the distance from the center of the object of mass M and the point you are interested in. Therefore the value of g increases as you move closer to the center of the Earth, so the gravitational force is at it's maximum when the block is at it's lowest point.

You are however correct in saying the maximum speed occurs at the equilibrium point, and you can argue that this is true from energy considerations without doing any calculations.

Edit: Forgot to mention, the distances that the block would move would be so small compared to the radius of the Earth that the force due to gravity may be treated as a constant.
 
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1. How do you calculate the maximum speed of a 2kg block on a spring?

The maximum speed of a 2kg block on a spring can be calculated using the formula v = √(k/m), where v is the maximum speed in meters per second, k is the spring constant in Newtons per meter, and m is the mass of the block in kilograms.

2. What is the spring constant and how does it affect the maximum speed of the block?

The spring constant is a measure of the stiffness of the spring and is represented by the letter k. It determines how much force is needed to stretch or compress the spring. As the spring constant increases, the maximum speed of the block also increases.

3. Can you calculate the maximum speed of the block without knowing the spring constant?

No, the spring constant is an essential component in the formula for calculating the maximum speed of the block. Without it, the calculation cannot be performed accurately.

4. How does the mass of the block affect the maximum speed on the spring?

The mass of the block, represented by the letter m, has an inverse relationship with the maximum speed. This means that as the mass increases, the maximum speed decreases, and vice versa.

5. What are the units for the maximum speed of the block on the spring?

The maximum speed of the block on the spring is typically measured in meters per second (m/s) since it is a measure of velocity. However, it can also be measured in other units such as kilometers per hour or miles per hour.

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