How High Was the Plunger Released to Compress the Springs?

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In summary, the conversation discusses the release of an 8-kg plunger from rest, stopped by two nested springs with constants k1 = 3kN/m and k2 = 10kN/m. The maximum deflection of the outer spring is observed to be 150mm and the height h from which the plunger was released can be determined by setting up equations based on energy conservation principles. The resulting height is 0.509m. There was a typo in the spring constant but the overall work and solution were deemed correct.
  • #1
JoshuaR
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1. An 8-kg plunger is released from rest in the position shown and is stopped by the two nested springs; the constant of the outer spring is k1 = 3kN/m and the constant of the inner spring is k2 = 1-kN/m. If the maximum deflection of the outer spring is observed to be 150mm, determine the height h from which the plunger was released.
Given a diagram. h is the height above the tallest spring, the outer spring. The outer spring is 90 mm higher than the inner spring.



2. mgh=PE .5kx^2=PE spring



3. mg(h+.15m) = .5k1(.15m^2) + .5k2(.06m^2)
Yielding an h of 0.509m.
Can someone inform me if this is the right path? It seems too simple...
 
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  • #2
Theres a typo in your spring constant so can't confirm answer but work looks fine.
 
  • #3
sorry, k1=3kN/m and k2=10kN/m if I remember correctly. Thanks for the confirmation.
 

FAQ: How High Was the Plunger Released to Compress the Springs?

How does gravity affect an object falling?

Gravity is a natural force that pulls objects towards the center of the Earth. When an object is dropped, it falls towards the ground because of the force of gravity. The speed at which the object falls is determined by the strength of the gravitational pull and the object's mass.

What is the relationship between an object's weight and its acceleration when it falls?

According to Newton's second law of motion, the acceleration of an object is directly proportional to the force applied to it and inversely proportional to its mass. This means that as an object's weight increases, its acceleration when falling also increases.

How do springs catch falling objects?

Springs work by exerting a force in the opposite direction of the applied force. When an object falls onto a spring, the spring will compress and push back against the object with an equal and opposite force, effectively catching the falling object.

Can the height from which an object falls affect how a spring catches it?

Yes, the height from which an object falls can affect how a spring catches it. This is because the force of gravity increases as the object falls, meaning that the object will have a greater speed and momentum when it reaches the spring. The spring will need to exert a stronger force to catch the object.

How does the elasticity of a spring impact its ability to catch objects?

The elasticity of a spring refers to its ability to return to its original shape after being stretched or compressed. A more elastic spring will have a greater ability to catch falling objects, as it can absorb and release energy more effectively. A less elastic spring may not be able to catch the object or may not be able to bounce it back as high as a more elastic spring would.

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