Spring Constants and compression

[anotherperson]

Homework Statement

A 5.0kg mass is hanging from a spring scale and is slowly lowered onto a vertical spring. The scale reads in Newtons.

a) what does the scale read when the mass is not in contact with the spring?
b)the scale reads 20N when the lower spring is compressed by 2.0cm. show that the value of the spring constant of the lower spring is 1450 N/m
c) by how much must the lower spring be compressed for the scaled to read 0.0N

Homework Equations

Fnet=ma
Fsp=-kdeltax

The Attempt at a Solution

a)F=5X9.8
=49N

b) 20=-kX2.0

but i get the wrong answer??

c) is i do
0=1450x
then x=0
?

 

[Fewmet]

Your answer to a) looks good.

Your answer to be would be correct if the spring were weightless, but you have calculated that it pulls down with a force of 49 N. How can you take that into account in b)?

For c), you must again allow for the 49 N that the scale reads when no weight is on it. I think you see you could make the scale read less if you push up of the spring. How hard would you ahve to push for it to read 0 Newtons?

 

[anotherperson]

for part b, I am still unsure how you factor in the 49N, i have a feeling you would add it but into what rule would you use these numbers, the rule i have used above?

so for part c you do 49N divided by the spring constant of 1450 and you get an answer of 3.38 cm which matches my answers, thanks!

 

[Doc Al]

b) 20=-kX2.0

but i get the wrong answer??

20 N is the reading on the spring scale, not the force compressing the vertical spring. If the spring scale reads 20 N, how much force must the vertical spring exert on the mass in order to support its weight?

(Hint: There are three forces acting on the mass. What are they? What must the net force be?)

 

[rwisz]

I would provide the following response:

a) When the mass is not in contact with the spring, the scale reads the weight of the mass, which is equal to the force of gravity acting on it. This can be calculated using the formula F=mg, where m is the mass and g is the acceleration due to gravity.

b) To find the spring constant, we can rearrange the formula Fsp=-kdeltax to solve for k. Plugging in the values given, we get:

20N=-k(0.02m)
k= -20N/0.02m
k= -1000N/m

However, since the question asks for the value of the spring constant of the lower spring, we need to take into account that there are two springs in this system. The upper spring, which is holding the mass, also contributes to the total spring constant. Therefore, we need to add the two spring constants together to get the total spring constant of the system.

Let's assume that the upper spring has a spring constant of k1, and the lower spring has a spring constant of k2. Then, the total spring constant (k) can be calculated as:

k= k1 + k2

We already know that k2= -1000N/m, so we can plug this into the equation:

1450N/m= k1 + (-1000N/m)

Solving for k1, we get:

k1= 2450N/m

Therefore, the value of the spring constant for the lower spring is 1450N/m.

c) To find how much the lower spring must be compressed for the scale to read 0N, we can use the same formula Fsp=-kdeltax. However, in this case, we are solving for the compression distance (deltax). Plugging in the values, we get:

0N= -1450N/m x deltax

Solving for deltax, we get:

deltax= 0m

This means that the lower spring must not be compressed at all for the scale to read 0N. This makes sense because if the lower spring is not compressed, then the force it exerts on the mass is equal to the force of gravity acting on the mass, resulting in a net force of 0N.