Maximum speed of a cylinder dropped on a spring

In summary, the conversation discusses the release of Cylinder A with a mass of 5kg from a height of 100mm above a spring with a stiffness of 1.8 kN/m. The maximum compression of the spring, spring deflection at maximum velocity, and maximum velocity of the cylinder are determined. However, there is some uncertainty about the accuracy of the calculation for maximum velocity as the correct answer is supposed to be 1.49 but the calculated answer is 1.4. The conversation ends with a question about the acceleration of the cylinder shortly after hitting the spring.
  • #1
Rajveer97
6
0

Homework Statement


Cylinder A (mass = 5kg) is released from rest at a height h =100mm above a spring of stiffness k = 1.8 kN/m. Determine, (i) the maximum compression of the spring, (ii) the spring deflection when the cylinder’s velocity is a maximum, and, (iii) the maximum velocity of the cylinder

I just need to confirm part iii

Homework Equations


Ep=mgh
Ek=(1/2)mv^2
Es=(1/2)kx^2
F=kx

The Attempt at a Solution


For part (i) I got 0.106
(ii) 27.2mm
For (iii) I did Ep=Ek which gave me v=1.4. The correct answer is supposed to be 1.49, I feel my answer is similar is wrong but similar just by chance. I just don't fully understand the question, when will the speed be maximum, before or after deflection? I feel before but I'm unsure.

Thanks
 
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  • #2
Hi,
You don't really specify what you did. Could there be a term missing in your 'doing'?
 
  • #3
BvU said:
Hi,
You don't really specify what you did. Could there be a term missing in your 'doing'?
Well I meant I basically made gravitational potential energy equal kinetic energy and solved for v
 
  • #4
Es ?
 
  • #5
Rajveer97 said:
I did Ep=Ek
What, roughly, is the cylinder's acceleration very shortly after hitting the spring?
 

Related to Maximum speed of a cylinder dropped on a spring

1. What factors affect the maximum speed of a cylinder dropped on a spring?

The maximum speed of a cylinder dropped on a spring is affected by several factors such as the mass and shape of the cylinder, the stiffness of the spring, and the height at which the cylinder is dropped. Other factors that may also influence the maximum speed include air resistance, surface friction, and the material properties of the cylinder and spring.

2. How is the maximum speed of a cylinder dropped on a spring calculated?

The maximum speed of a cylinder dropped on a spring can be calculated using the equation v = √(2gh), where v is the maximum speed, g is the acceleration due to gravity, and h is the height at which the cylinder is dropped. This equation is based on the conservation of energy principle, which states that the potential energy of an object at a certain height is converted into kinetic energy at the bottom of its fall.

3. Can the maximum speed of a cylinder dropped on a spring be greater than the initial speed?

No, the maximum speed of a cylinder dropped on a spring cannot be greater than the initial speed. This is because the maximum speed is determined by the height at which the cylinder is dropped and is independent of the initial speed. However, if external forces such as air resistance or friction act on the cylinder, the maximum speed may be lower than the calculated value.

4. How does the maximum speed of a cylinder dropped on a spring change with the stiffness of the spring?

The maximum speed of a cylinder dropped on a spring is directly proportional to the stiffness of the spring. This means that a stiffer spring will result in a higher maximum speed, while a less stiff spring will result in a lower maximum speed. This relationship can be explained by Hooke's Law, which states that the force exerted by a spring is directly proportional to its stiffness.

5. What is the significance of studying the maximum speed of a cylinder dropped on a spring?

The study of the maximum speed of a cylinder dropped on a spring is important in understanding the behavior of objects in motion and the principles of energy conservation. It also has practical applications in fields such as engineering and physics, where knowledge of the maximum speed can help in designing and optimizing systems involving springs and falling objects.

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