Total work done on clay during Spring Compression

In summary, the problem involves a 4.63-kg ball of clay being thrown downward from a height of 2.69 m with a speed of 5.01 m/s onto a spring with a spring constant of 1610 N/m. The clay compresses the spring a maximum amount of 0.50230 m before momentarily stopping. The total work done on the clay during the spring's compression can be found using the equation W = Ks + Ub, where Ks is the spring potential energy and Ub is the ball's gravitational potential energy. After plugging in the values, the correct answer is -180.3 J.
  • #1
Koscher
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Homework Statement



A 4.63-kg ball of clay is thrown downward from a height of 2.69 m with a speed of 5.01 m/s onto a spring with k = 1610 N/m. The clay compresses the spring a certain maximum amount before momentarily stopping.

b) Find the total work done on the clay during the spring's compression.

Homework Equations



Us=integral(-kx dx)

The Attempt at a Solution



From part of the question I found the maximum compression of the spring to be 0.50230 m, and I know that is correct.

I thought that the total amount of work done on something by the spring's compression was equal to the integral that is in the relevant equations section.

Therefore, that is what I did. I Us=integral(-kx dx) from 0 to 0.50230. The resulting answer was -203.106 J. But that is not correct, does anyone have some insight to what went wrong?
 
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  • #2
Nevermind, i figured it out.

W = Ks + Ub

W=(-1/2)(1610)(0.502302) + (4.63)(9.81)(0.50230)

W= -180.3 J
 

What is "total work done on clay during Spring Compression"?

"Total work done on clay during Spring Compression" refers to the amount of energy that is exerted on a piece of clay when it is compressed by a spring. This can be calculated by multiplying the force applied to the clay by the distance the clay was compressed.

Why is it important to measure the total work done on clay during Spring Compression?

Measuring the total work done on clay during Spring Compression is important because it allows us to understand the physical properties of the clay, such as its elasticity and strength. This information can be useful in various fields, such as materials science and engineering, as well as in the manufacturing of products made from clay.

What factors can affect the total work done on clay during Spring Compression?

The total work done on clay during Spring Compression can be affected by a variety of factors, such as the type and quality of the clay, the design and strength of the spring, and the amount of force applied to the clay. Other factors, such as temperature and humidity, can also play a role in the total work done on the clay.

How is the total work done on clay during Spring Compression measured?

The total work done on clay during Spring Compression is typically measured using a device called a force gauge, which measures the amount of force applied to the clay. The distance the clay is compressed can be measured using a ruler or other measuring tool. The total work done can then be calculated by multiplying the force by the distance.

How can the total work done on clay during Spring Compression be used in practical applications?

The total work done on clay during Spring Compression can be used in various practical applications, such as in the design of clay-based products, determining the strength of different types of clay, and in understanding the behavior of clay under different conditions. This information can also be useful in the development of new materials and products that utilize clay as a component.

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