How Is Work Calculated When a Block Compresses a Vertical Spring?

In summary, a 315.0 g block is dropped onto a vertical spring with a spring constant k = 262.0 N/m. The block becomes attached to the spring, and the spring compresses 0.12 m before momentarily stopping. The work done by the block's weight is 1.886N*m and the work done by the spring is also 1.886N*m. The speed of the block just before it hit the spring can be found using the conservation of energy principle and the formula for gravitational energy.
  • #1
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Homework Statement


A 315.0 g block is dropped onto a vertical spring with a spring constant k = 262.0 N/m. The block becomes attached to the spring, and the spring compresses 0.12 m before momentarily stopping. While the spring is being compressed, what work is done by the block's weight?

What work is done by the spring?

What was the speed of the block just before it hit the spring?


Homework Equations


Us = 1/2kx^2


The Attempt at a Solution


Us = 1/2 * 262 *.12^2
 
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  • #2
Should be right, what is your question?
 
  • #3
That is the work done by the spring right? Because it's saying it's wrong. I am getting an answer of 1.886N*m.
 
  • #4
I don't understand why that equation is not working.
 
  • #5
Are you sure that the units are all what you posted? Does it want you to define your zero potential in a certain way, has it located the origin for you, i.e. might it care about signs?

Yes,

F_s = -kx, so W_s = U_s = integral(-dU) = integral(-kx) = .5*kx^2
 
  • #6
oh ok I got it..so for part do you just multiply that by the weight of the block?
 
  • #7
You mean how do you find the speed of the block? It screams conservation of energy.
 
  • #8
Ug = mgy

So is it just the formula for gravitational energy?
 
  • #9
does anyone know the answer to this problem? I have the same issue... One thing to remember they block is being dropped from a height above the spring and then it compresses the spring so I need to find a way to find that height before it comes in contact with the spring
 

What is vertical spring work done?

Vertical spring work done is the amount of energy required to stretch or compress a spring in a vertical direction. This can be calculated by multiplying the force applied to the spring by the distance it is stretched or compressed.

How is vertical spring work done measured?

Vertical spring work done is typically measured in joules (J) or newton-meters (N*m). This can be calculated using the formula W = Fd, where W is the work done, F is the applied force, and d is the distance the spring is stretched or compressed.

What factors affect the amount of vertical spring work done?

The amount of vertical spring work done is affected by the force applied to the spring, the distance it is stretched or compressed, and the stiffness of the spring. The stiffer the spring, the more work required to stretch or compress it.

How is vertical spring work done related to potential energy?

Vertical spring work done is directly related to potential energy. When a spring is stretched or compressed, it gains potential energy, which is equal to the amount of work done on the spring. This potential energy can then be converted into other forms of energy, such as kinetic energy, when the spring is released.

What are some real-life applications of vertical spring work done?

Vertical spring work done has many applications in everyday life, such as in trampoline jumping, pogo sticks, and shock absorbers in vehicles. It is also used in various industrial and mechanical systems, such as in springs for door hinges or in mechanical watches.

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