Understanding Signs of Net Force in Mass-Spring Systems

In summary, the conversation is discussing the signs of net force of a mass on a spring and how to equate them based on different sign conventions. It is clarified that at the equilibrium position, the net force on the mass is zero. The minus sign in Hooke's law indicates the direction of the restoring force with respect to displacement x. The magnitude of the force is always kx, but the sign used depends on the coordinate system and sign convention.
  • #1
chattymatty
2
0
Hello!

I am having trouble with a simple concept...trying to figure out the signs of net force of a mass on a spring.

I understand that for a mass on the spring, there is a downward force of gravity (mg) and upwards restoring force of the (-kx). How do we equate these, if we regard the positive direction in the same direction as gravity? How would we equate these, if we, in contrast, regard the positive direction in the same direction as the restoring force?

I believe that the final conclusion will be mg = kx. But where are the signs? How did the signs cancel out?

Thank you!
Chatty Matty
 
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  • #2
At the equilibrium position, the net force on the mass is zero.

The thing to realize is that regardless of sign convention the spring force acts up (magnitude kx, where x is the distance below the unstretched position) and gravity acts down. What might be throwing you off is the minus sign in Hooke's law: F = -kx. The minus sign just tells you the direction of the restoring force with respect to displacement x. (If x is down, F is up.)

Using up as positive, the spring force is +kx and gravity is -mg. Add them up to get: kx - mg = 0.

Using down as positive, the spring force is -kx and gravity is +mg. Add them: -kx + mg = 0.
 
  • #3
Hi Doc Al,

When considering the forces, how come we did not consider the minus sign in Hooke's law? So when we consider the spring force (whether we take up or down being positive), is the spring force just "kx"? Depending on the direction we take as positive/negative will dictate then the a +kx or -kx, and not from Hooke's law?

Thanks!
 
  • #4
Hooke's law tells you the actual direction of the force. (Not by blinding plugging into the equation, but by understanding it.) The force is always opposite to the direction of the stretch (or compression) with respect to the unstretched position. If you pull the spring in one direction, the restoring force points in the opposite direction.

The magnitude of that force is always just kx (where x is taken as positive); the sign that you use depends on the coordinate system and sign convention that you are using.
 

1. What is a mass spring constant?

The mass spring constant, also known as the spring constant or stiffness, is a physical property that describes the stiffness of a spring. It is represented by the symbol k and is measured in units of force per unit length, such as N/m or lbs/in.

2. How is the mass spring constant calculated?

The mass spring constant is calculated by dividing the applied force by the displacement of the spring. This is known as Hooke's Law, which states that the force applied to a spring is directly proportional to the spring's displacement.

3. What factors affect the mass spring constant?

The mass spring constant is affected by several factors, including the material and dimensions of the spring, the number of coils, and the type of end attachments. It can also be affected by external factors such as temperature and stress.

4. What is the significance of the mass spring constant in physics?

The mass spring constant is an important concept in physics as it helps us understand the behavior of springs and elastic materials. It is also used in various applications, such as designing and analyzing mechanical systems and structures, and in fields like seismology and acoustics.

5. How does the mass spring constant impact the motion of an object?

The mass spring constant affects the motion of an object by determining how much force is required to stretch or compress the spring. A higher mass spring constant indicates a stiffer spring, which will require more force to produce the same amount of displacement. This can impact the overall motion and stability of the object.

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