How Does Changing the Length of a Meter Stick Affect Its Oscillation Period?

In summary, the first problem involves a meter stick hanging from a thin wire and being rotated clockwise. The meter stick is then sawed off and set in oscillation, and the question asks for the period of this oscillation. The second problem involves a person jumping onto a fire net and calculating the amount of stretch using the equation mgh = 0.5kx^2. Additional information about the wire's length and the point of contact between the meter stick and the wire is needed for the first problem.
  • #1
squib
40
0
2 Questions, pretty stumped on both.
A meter stick is hung at its center from a thin wire (see part (a) of the figure below).

Meter stick is hanging from a string, and being "rotated clockwise.


It is twisted and oscillates with a period of 6.18 s. The meter stick is sawed off to a length of 68.1 cm. This piece is again balanced at its center and set in oscillation (b). With what period does it oscillate?

Not really even sure where to start on this one... still looking at it.

Next:A 56.8 kg person jumps from a window to a fire net 21.8 m below, which stretches the net 1.25 m. Assume that the net behaves like a simple spring, and calculate how much it would stretch if the same person were lying in it.

Tried mgh = .5kx^2, then used F/k=x, but this didn't work, any ideas?
 
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  • #2
squib said:
2 Questions, pretty stumped on both.
A meter stick is hung at its center from a thin wire (see part (a) of the figure below).

Meter stick is hanging from a string, and being "rotated clockwise.


It is twisted and oscillates with a period of 6.18 s. The meter stick is sawed off to a length of 68.1 cm. This piece is again balanced at its center and set in oscillation (b). With what period does it oscillate?

Not really even sure where to start on this one... still looking at it.

Next:A 56.8 kg person jumps from a window to a fire net 21.8 m below, which stretches the net 1.25 m. Assume that the net behaves like a simple spring, and calculate how much it would stretch if the same person were lying in it.

Tried mgh = .5kx^2, then used F/k=x, but this didn't work, any ideas?

We need a better idea what the first problem is. Does the thin wire have some length, and does it move in the problem? Is the point of contact bwteen the meter stick and the wire stationary?

Your second problem sounds like you have the right idea. Did you include the stretch in your h?
 
  • #3
Good call on that second one, forgot to add h from stretch.

On the first one. The wire is stationary, no length given. The meter stick is hung by the middle, and a force is applied to make it spin in a plane horizontal to the ground, at least that is my understanding of the problem.

Any ideas?
 

Related to How Does Changing the Length of a Meter Stick Affect Its Oscillation Period?

1. What is a spring constant?

A spring constant, also known as a spring stiffness, is a measure of the force required to stretch or compress a spring by a certain distance.

2. How is a spring constant calculated?

The spring constant is calculated by dividing the force applied to the spring by the distance the spring is stretched or compressed. This is known as Hooke's Law, which states that the force applied is directly proportional to the displacement.

3. What units are used to measure spring constant?

The units used to measure spring constant depend on the system of units being used. In the International System of Units (SI), the unit of spring constant is Newtons per meter (N/m). In the British engineering system, the unit is pounds-force per inch (lbf/in).

4. How does the spring constant affect the behavior of a spring?

The higher the value of the spring constant, the stiffer the spring is. This means that a higher force is required to stretch or compress the spring by a certain distance. On the other hand, a lower spring constant indicates a less stiff spring that requires less force to be stretched or compressed.

5. Can the spring constant of a spring be changed?

Yes, the spring constant of a spring can be changed by altering its physical properties such as its length, diameter, or material. For example, increasing the length of a spring will decrease its spring constant, making it less stiff. Similarly, changing the material of the spring to a more rigid one will increase its spring constant.

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