Spring Energy (Finding Velocity)

In summary, the problem involves a spring with a constant of 2N/m attached to a support and a collar with mass 1kg. The collar is released from rest at 0.9m and travels along a horizontal rod with a length of 1.2m. The question asks for the magnitude of the collar's velocity at point C, neglecting friction. The solution involves using the equations for kinetic and potential energy, and correctly accounting for the work done by the spring.
  • #1
Sam Fred
15
0

Homework Statement


A spring AB or constant k = 2N/m is attached to a support A and to a collar of mass
m=1kg. The unstretched length of the spring is 1m, Knowing that the collar is released
from rest at x = x0 = 0.9 m and neglecting friction between the collar and the horizontal
rod, determine the magnitude of the velocity of the collar as it passes through point C.
here l = 1.2m,

Homework Equations


T1 + U1-2 = T2
T Kinetic Energy
U Potential Energy

The Attempt at a Solution


I just wanted to see if the answer is right ??
IMG_0872.jpg
 
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  • #2
Looks okay.
 
  • #3
I don't think you handled the work done by the spring correctly. It is not k(.3)2/2.
 
  • #4
I don't see it... I thought he was correct noting the length of the spring changes from 1.5m to 1.2m.
 
  • #5
x22-x12 ≠ (x2-x1)2
 
  • #6
Now I see it...thanks.
 

1. How does spring energy relate to velocity?

Spring energy is directly related to velocity through Hooke's Law, which states that the force exerted by a spring is proportional to the displacement of the spring from its equilibrium position. As the displacement of the spring increases, the force applied also increases, resulting in an increase in velocity.

2. How is the velocity of an object calculated using spring energy?

The velocity of an object can be calculated using the equation: v = √(2kx/m), where v is the velocity, k is the spring constant, x is the displacement of the spring, and m is the mass of the object. This equation is derived from the conservation of energy principle.

3. Can spring energy be converted into other forms of energy?

Yes, spring energy can be converted into other forms of energy such as kinetic energy, potential energy, and thermal energy. When a spring is compressed, it stores potential energy, which is then converted into kinetic energy as the spring expands and moves the object attached to it. Friction between the spring and the object can also convert some of the energy into thermal energy.

4. How does the spring constant affect the velocity of an object?

The spring constant, denoted by k, is a measure of the stiffness of a spring. A higher spring constant means that the spring is stiffer and thus, more force is required to produce the same amount of displacement. This results in a higher velocity for the object attached to the spring.

5. Is it possible to calculate the velocity of an object using spring energy if the mass is unknown?

No, the mass of the object is a crucial factor in calculating velocity using spring energy. Without knowing the mass, the equation v = √(2kx/m) cannot be solved. However, if the object's weight is known, it can be used to estimate the mass and calculate the velocity.

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