What is the relationship between spring stiffness and length?

[jsmith613]

Homework Statement

look at attachment

Homework Equations

The Attempt at a Solution

so we know that the frequency of a spring is given by
$f = \frac{1}{2 pi} \sqrt{\frac{k}{m}}$

so the answer should be A
BUT the answer is C. why?

 

[collinsmark]

Why do you think the answer should be A? How would adding an inelastic string affect the variables described by the
$$f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$$
equation?

 

[jsmith613]

Why do you think the answer should be A? How would adding an inelastic string affect the variables described by the
$$f = \frac{1}{2 \pi} \sqrt{\frac{k}{m}}$$
equation?

surely it affects spring consttant?

 

[jsmith613]

how does changing the length of the spring change k??
although F = kx
F/x is constant for a particular string

 

[PeterO]

how does changing the length of the spring change k??
although F = kx
F/x is constant for a particular string

A strong spring will be extended a small amount when a load m is attached.
A weak spring will be extended a large amount when a load m is attached.

Suppose the original spring was extended 10cm by the load m
That means each half was extended 5 cm by the load m.

Thus in example C, the load m extends the piece of spring only 5cm. the half spring behaves as a stronger spring that the whole spring.

In example D, each of the springs will be extended 10cm by the load - so a total extension of 20cm. The double spring behaves as a weaker spring than a single spring.

 

[jsmith613]

A strong spring will be extended a small amount when a load m is attached.
.

so basically I have to know that a shorter spring is stiffer than a longer spring?

 

[PeterO]

so basically I have to know that a shorter spring is stiffer than a longer spring?

To say that short springs are stiffer than long springs is not strictly correct.
I think you will find that the 30 cm spring from the front suspension of a car is much stiffer than the 10cm spring in a laboratory "spring balance"

Instead, you have to note that when a spring is stretched by a load, a fraction of that spring stretches only a fraction of that amount.

When that is applied to compute a spring constant, it means that if you have two sections of the same original spring, the shorter section will have a higher spring constant.

When you study materials, you will come across the concept of Young's Modulus. That is a measure that is used to show that two samples have basically the same material properties, despite the fact that one of them is extended more in an absolute sense.

 

[jsmith613]

To say that short springs are stiffer than long springs is not strictly correct.
I think you will find that the 30 cm spring from the front suspension of a car is much stiffer than the 10cm spring in a laboratory "spring balance"

Instead, you have to note that when a spring is stretched by a load, a fraction of that spring stretches only a fraction of that amount.

When that is applied to compute a spring constant, it means that if you have two sections of the same original spring, the shorter section will have a higher spring constant.

When you study materials, you will come across the concept of Young's Modulus. That is a measure that is used to show that two samples have basically the same material properties, despite the fact that one of them is extended more in an absolute sense.

cheers