Finding the Spring Constant of a ball

In summary, the problem involves a spring shooting a 20 g ball horizontally. When the spring is compressed 18 cm, the ball travels horizontally 5.1 m and lands on the floor 1.7 m below the point at which it left the spring. To determine the spring constant, the initial velocity must be calculated using the time it takes for the ball to drop 1.7 m. The horizontal velocity can then be determined and used to find the kinetic energy of the ball. Knowing the kinetic energy, the potential energy initially in the spring can be calculated, allowing for the determination of the spring constant. The ball's vertical motion does not affect the calculation of the spring constant, only its horizontal displacement.
  • #1
ckrup
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1. A spring clamped to a table shoots a 20 g ball horizontally. When the spring is compressed 18 cm the ball travels horizontally 5.1 m and lands on the floor 1.7 m below the point at which it left the spring. What is the spring constant (in N/m)

2. I tried using k=mg/x (x being distance of the spring compression) but am at a COMPLETE loss as how to solve it!
 
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  • #2
ckrup said:
1. A spring clamped to a table shoots a 20 g ball horizontally. When the spring is compressed 18 cm the ball travels horizontally 5.1 m and lands on the floor 1.7 m below the point at which it left the spring. What is the spring constant (in N/m)

2. I tried using k=mg/x (x being distance of the spring compression) but am at a COMPLETE loss as how to solve it!

Welcome to PF.

This is a double problem.

First find the initial velocity, which is totally in the x direction.

You do that by figuring the time for it to drop 1.7 m.

Take that time and determine horizontal velocity by 5.1 m / Time to drop.

Now for part 2:
You know the V so you know KE which is mV2/2

If you know KE then you know how much PE was initrially in the spring by PE = k*x2/2

You know x, you know PE now you can finally know k.
 
  • #3
i have a similar problem to this one and am stuck. Isn't the ball moving in the y direction also since it falls below where it left the spring?
 
  • #4
ineedhelp1 said:
i have a similar problem to this one and am stuck. Isn't the ball moving in the y direction also since it falls below where it left the spring?

Welcome to PF.

Yes. Gravity does develop a y component of velocity. But the x component only is the initial velocity and it is this velocity that determines how far from the table it lands.

The Vx * t is that distance. Hence the importance of calculating the t in order to determine that distance.
 

FAQ: Finding the Spring Constant of a ball

1. What is the Spring Constant of a ball?

The Spring Constant of a ball, also known as the spring stiffness, is a measure of the elasticity of the ball. It represents the force required to compress or stretch the ball by a certain distance. It is usually denoted by the symbol "k" and its unit is Newtons per meter (N/m).

2. How is the Spring Constant of a ball determined?

The Spring Constant of a ball can be determined by conducting a simple experiment where a known force is applied to the ball and the resulting displacement is measured. The ratio of the applied force to the resulting displacement is the Spring Constant. This can be done using Hooke's Law, which states that the force applied to an elastic object is directly proportional to the amount of stretch or compression.

3. What factors affect the Spring Constant of a ball?

The Spring Constant of a ball can be affected by various factors such as the material of the ball, the shape and size of the ball, and the temperature. Generally, stiffer materials have a higher Spring Constant, while softer materials have a lower Spring Constant. Additionally, larger and more spherical balls tend to have a higher Spring Constant compared to smaller or irregularly shaped balls.

4. Why is it important to know the Spring Constant of a ball?

The Spring Constant of a ball is important because it helps us understand the behavior of the ball when it is subjected to external forces. It can also be used to predict the amount of deformation or compression that will occur in the ball when a certain force is applied. This information is crucial in various fields such as sports, engineering, and physics.

5. Can the Spring Constant of a ball change?

Yes, the Spring Constant of a ball can change depending on the factors that affect it, such as the material, shape, and temperature. It can also change if the ball is damaged or undergoes wear and tear. It is important to note that the Spring Constant is not a constant value, but rather a measure of the ball's elasticity in a specific moment.

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