Why is the height of the table not necessary to solve this problem?

In summary, the problem states that the gun is mounted on a table and that the target is on the floor. You don't need the height of the table to solve this problem. I strongly suggest that you adopt an algebraic approach, i.e. use symbols and not numbers when you write equations. Use symbols for unknown quantities and don't worry if you don't have numbers for them. It will all come out in the wash.
  • #1
jolly_math
51
5
Homework Statement
Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring-loaded gun that is mounted on a table. The target box is 2.20 m horizontally from the edge of the table. Bobby compresses the spring 1.10 cm, but the marble falls 27.0 cm short. How far should Rhoda compress the spring to score a hit?
Relevant Equations
U(x) = (1/2)kx^2
KE = (1/2)mv^2
Ki + Ui = Kf + Uf
1/2)kx2 = (1/2)mvf2, but W = (1/2)mvf2 = F∆d, so
1/2)kx^2 = F∆d.

The solution says that I should just substitute v as d/t. But could anyone explain why my reasoning is wrong? Thanks.
 
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  • #2
Which force is this that does the work W = FΔd? What is the direction of F relative to the direction of the displacement Δd? This is a projectile motion problem where you need to find the initial speed of the projectile needed to hit the target. Then you must match that speed to the spring compression.
 
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  • #3
So, I'm taking it that the spring gun must be horizontal, and the target has no vertical dimension ( physical size)?
 
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  • #4
erobz said:
So, I'm taking it that the spring gun must be horizontal, and the target has no vertical dimension?
1666651983080.png

This is the diagram. I just assumed there was no vertical dimension, as the solution didn't consider it and I'm not sure how to calculate it otherwise.
 
  • #5
jolly_math said:
View attachment 316004
This is the diagram. I just assumed there was no vertical dimension, as the solution didn't consider it and I'm not sure how to calculate it otherwise.
That is the only configuration I could find a solution for with the information given.

Have you worked it out the approach yet?
 
  • #6
jolly_math said:
View attachment 316004
This is the diagram. I just assumed there was no vertical dimension, as the solution didn't consider it and I'm not sure how to calculate it otherwise.
The problem states that the gun is mounted on a table and that the target is on the floor. You don't need the height of the table to solve this problem. I strongly suggest that you adopt an algebraic approach, i.e. use symbols and not numbers when you write equations. Don't worry if you don't have numbers for the symbols. It will all come out in the wash.
 
  • #7
kuruman said:
The problem states that the gun is mounted on a table and that the target is on the floor. You don't need the height of the table to solve this problem. I strongly suggest that you adopt an algebraic approach, i.e. use symbols and not numbers when you write equations. Use symbols for unknown quantities and don't worry if you don't have numbers for them. It will all come out in the wash.
I was just indicating that a diagram wasn't posted. It was my lack of being able to find a solution for some arbitrary gun angle that led me to conclude that it must be this way.

You don't need the height of the table to solve this problem.
I was talking about the height of the target, as in its physical dimensions. Not where it is located spatially. That was probably confusing, but the OP seemed to understand what I was asking.

Anyhow, It sounds as though the @jolly_math has figured it out.
 

FAQ: Why is the height of the table not necessary to solve this problem?

What is potential energy?

Potential energy is the energy that an object possesses due to its position or configuration. It is stored energy that can be converted into other forms, such as kinetic energy.

How is potential energy related to springs?

When a spring is stretched or compressed, it stores potential energy in the form of elastic potential energy. This is because the spring is exerting a force that is trying to return it to its original, unstretched position.

What is Hooke's Law?

Hooke's Law is a principle that describes the relationship between the force applied to a spring and the resulting displacement of the spring. It states that the force applied is directly proportional to the displacement of the spring.

What is the equation for calculating potential energy in a spring?

The equation for calculating potential energy in a spring is PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement from the equilibrium position.

How can potential energy in a spring be changed?

Potential energy in a spring can be changed by altering the displacement of the spring or by changing the spring constant. The potential energy will increase as the displacement or spring constant increases, and decrease as they decrease.

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