A spring is attached to the ceiling by a string with no weights

[vstrimaitis]

1. A cylindrical string is made out of thin wire.

• The distance between every loop of an unstretched spring is equal;

• The radius of every loop of the spring is r = 4 cm;

• The length of an unstretched spring is l = 20 cm;

• The mass of the spring is m = 50 g;

The spring is hung on the ceiling by a non-elastic string which has a length of a = 10 cm. When the string is hanging, it has the length of l' = 25 cm.

2.

• What is the constant of the spring (k)?

• What is the period of this system, if the angle, at which it is released, is small?

3. I haven't really solved any problems when the weight is not attached on the end of the spring. Does it work the same way or not? If it does, I'll be able to find k. But I have no idea what to do with the period... Any help at all would be appreciated ^^

 

[mfb]

Please add a sketch of the system. It is hard to visualize this based on your post.
If something is connected to a point within the spring, you can split the spring in two pieces and consider them as two springs.

 

[vstrimaitis]

Please add a sketch of the system. It is hard to visualize this based on your post.
If something is connected to a point within the spring, you can split the spring in two pieces and consider them as two springs.

I hope this will clarify the problem at least a little bit.

 

[mfb]

Then you'll have to consider the weight of the spring. For a length x in the unstretched spring (where you need some definition of x), what is the mass below that point? What is the stretching force there? If the total spring has a constant of D, what can you say about each point, and finally the stretching of the whole spring?

 

[Nickie]

1. Based on the given information, we can calculate the spring constant (k) using the formula k = mg/l', where m is the mass of the spring and l' is the length of the spring when it is hanging. Plugging in the values, we get k = (0.05 kg)(9.8 m/s^2)/(0.25 m) = 1.96 N/m.

The period of the system can be calculated using the formula T = 2π√(m/k), where m is the mass of the spring and k is the spring constant. In this case, the period would be given by T = 2π√(0.05 kg/1.96 N/m) = 0.8 s.

2. The spring constant (k) can be found by using the formula k = mg/l', where m is the mass of the spring and l' is the length of the spring when it is hanging. Plugging in the values, we get k = (0.05 kg)(9.8 m/s^2)/(0.25 m) = 1.96 N/m.

The period of the system can be calculated using the formula T = 2π√(m/k), where m is the mass of the spring and k is the spring constant. In this case, the period would be given by T = 2π√(0.05 kg/1.96 N/m) = 0.8 s.

3. The spring will behave the same way whether there is a weight attached to the end or not. The spring constant (k) will remain the same, as it is a characteristic of the spring itself and not affected by any external factors. The only difference would be in the mass (m) of the system, which would change depending on whether there is a weight attached or not. The period of the system would also change, as it is affected by both the mass and the spring constant.