Does Mass of Cart Affect Spring Extension?

In summary, the conversation discusses a physics concept involving the effect of mass on the extension of a spring. The equations and attempt at a solution are provided, but there is confusion about which object to analyze and the role of mass in the equation. It is concluded that adding the cart does not affect the stretch of the spring due to the constancy of the hanging mass.
  • #1
kay123
3
0

Homework Statement



I'm writing a paper on one of my lab experiments and I'm not sure my physics concept is right? The question asks if the mass of a cart affects the extension of the spring. A spring is attached to a cart which is attached to sting through a pulley and connected to a hanging object of mass W (a picture is attached). From my results, the spring stretched slightly more with the cart than without the cart attached to the spring.

Homework Equations



I know that at equilibrium all forces equal 0. Σ Fx = Σ Fy = 0
Fs= kx
F=mg

(with cart)
Σ Fx = Fs –Th
Σ Fy = Tv + Fn - Mgw -Mgc

(without cart)
Σ Fx = Σ Fx = Fs –Th
Σ Fy = Tv - Mgw

The Attempt at a Solution



If k is constant and Fs= kx and F=mg then mg=kx. Then if the cart was attached, mass will increase, therefore x (the spring extension) will increase, which explains why the spring stretched more when the cart was attached.

Is this somewhat right, because he said i have the wrong concept? Can anyone help me? Am I missing something?
 

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  • #2
kay123 said:
with cart)
Σ Fx = Fs –Th
Σ Fy = Tv + Fn - Mgw -Mgc

(without cart)
Σ Fx = Σ Fx = Fs –Th
Σ Fy = Tv - Mgw
This is a bit confused since it's not clear what object you are analyzing. You don't just add up all the forces that appear in a problem, you must pick an object (the cart or the end of the spring) and analyze the forces acting on it.
If k is constant and Fs= kx and F=mg then mg=kx.
Then if the cart was attached, mass will increase, therefore x (the spring extension) will increase, which explains why the spring stretched more when the cart was attached.
Here "m" is the hanging mass, which doesn't change when the cart is attached. So adding the cart would not affect the stretch of the spring.
 
  • #3




Your understanding of the concept is partially correct. The mass of the cart does indeed affect the extension of the spring, but it is not the only factor at play. The spring constant (k) and the force applied to the spring (Fs) also play a role in determining the amount of extension.

In your experiment, you observed that the spring stretched more when the cart was attached. This is because the mass of the cart added an additional force (Mgc) to the system, which in turn increased the overall force applied to the spring (Fs). This increase in force caused the spring to stretch more.

However, your equation of Fs=kx is only valid when there is no external force acting on the system. In this case, there is an external force (Mgc) acting on the system, which means the equation becomes Fs=kx+Mgc. This means that the increase in force (Mgc) will also contribute to the increase in spring extension.

In conclusion, the mass of the cart does affect the extension of the spring, but it is not the only factor. The spring constant and the external force also play a role in determining the amount of extension. It is important to consider all factors when analyzing the results of your experiment.
 

What is the relationship between the mass of a cart and spring extension?

The mass of a cart does affect spring extension. As the mass of the cart increases, the spring will extend more.

How does increasing the mass of the cart affect the spring constant?

Increasing the mass of the cart does not affect the spring constant. The spring constant is a physical property of the spring and remains constant regardless of the mass of the cart.

Does the spring extension depend on the type of spring used?

Yes, the spring extension can depend on the type of spring used. Different springs may have different spring constants and can affect the amount of extension for a given mass.

What other factors can affect spring extension?

Aside from the mass of the cart and the type of spring used, other factors that can affect spring extension include the force applied to the spring, the length of the spring, and any external forces acting on the spring.

How can we measure the spring extension caused by a cart?

The spring extension can be measured by using a ruler or a tape measure to measure the distance between the two ends of the spring before and after the cart is placed on it. The difference in these two measurements will give the spring extension caused by the cart.

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