Force of 1.5kg Crate Falling onto Spring Scale

The sum of those two is the compression.In summary, a 1.5kg crate falls from a height of 2.0m and reaches a potential energy of 30J. The industrial spring scale with a spring constant of 1.5 X 10^5 N/m measures the compression at its greatest point. To solve this problem, you can use two conservation of energy problems to find the kinetic energy and potential energy of the spring. This will give you the total compression of the crate.
  • #1
blackout85
28
1
A 1.5kg crate falls from a height of 2.0m onto an industrial spring scale with a spring constant of 1.5 X 10^5 N/m. At its greatest compression the reading on the scale is:

My work:

mgh= PE
(1.5kg*9.81m/s*2.0m)= 30J
The potential energy of the crate is 30J
The Force of the crate is 1.5kg* 9.81m= 14.75
Would the force of the crate be equal to the force of compression

Thank you
 
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  • #2
I'm not sure what you mean by "force of the crate." I also don't think using forces is a good way to solve this problem. You did a good job finding the PE at the top.

There are two ways to go from here. The better way (and also the slow way) is to turn it into two conservation of energy problems: first find the KE it attains just before hitting the spring, then find the PE of the spring after it comes to a stop.
 
  • #3
for your question. Based on the information provided, it appears that the force of the crate and the force of compression would be equal. This is because the potential energy of the crate is converted into kinetic energy as it falls, and then into elastic potential energy as it compresses the spring. According to the law of conservation of energy, energy cannot be created or destroyed, only transferred from one form to another. Therefore, the force of the crate would be equal to the force of compression on the spring scale.
 

1. How does the weight of the crate affect the reading on the spring scale?

The weight of the crate directly affects the reading on the spring scale. As the crate falls onto the spring scale, it exerts a downward force on the scale, causing the spring inside to compress. The degree of compression is directly proportional to the weight of the crate, so a heavier crate will result in a higher reading on the scale.

2. What is the relationship between force and acceleration in this scenario?

According to Newton's Second Law of Motion, the force exerted on an object is equal to its mass multiplied by its acceleration. In this scenario, the force of the crate falling onto the spring scale is equal to its mass (1.5kg) multiplied by the acceleration due to gravity (9.8 m/s^2), resulting in a force of 14.7 Newtons.

3. Will the reading on the spring scale change if the crate falls at a different speed?

No, the reading on the spring scale will not change based on the speed at which the crate falls. As long as the crate has a mass of 1.5kg, the force exerted on the scale will be the same regardless of how fast it is falling.

4. How does the spring inside the scale work to measure force?

The spring inside the scale works based on Hooke's Law, which states that the force applied to a spring is directly proportional to the amount of compression or extension of the spring. As the crate falls onto the scale, the spring inside compresses, and the degree of compression is measured and converted into a numerical value on the scale.

5. Is there a limit to the amount of force that the spring scale can measure?

Yes, there is a limit to the amount of force that the spring scale can measure. Every spring has a maximum amount of compression or extension that it can handle before it reaches its elastic limit and cannot return to its original shape. Once this limit is reached, the reading on the scale will no longer be accurate. It is important to use a spring scale that is appropriate for the amount of force being measured.

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