A spring has a force constant of 100N/m and an unstretched lenght of .07 m. One end is attached to a post that is free to rotate in the center of a smooth table. The other end is attatched to a 1 kg disc moving in uniform circular motion on the table, which stretches the spring by .03m. Friction is negligible. What is the centripital force on the disc?
a).3 N
b)3 N
c)10 N
d)300 N
e)1,000 N
So for the 1st part:to find the force I did this 100/.03 but I got 333.333 I can't figure out what i am doing wrong.
There's also a second part to this: What is the work done on the disc by the spring during one full circle?
a)0 J
b)94 J
c)186 J
d)314 J
e)628 J
Would I use W =fd where f is the answer of the above question times (.1)?
What you are doing wrong is not using Hooke's law: Force= k x
On the second, you are not thinking: W=fd is force times the distance in the direction of the force. The direction is Perpendicular to the force, so work is zero.
F=kx
k=100
x=.03
F=100*.03=3N
(directed towards center b/c Centrip. force always does that)
To find the centripetal force on the disc, you first need to find the spring force when it is stretched by 0.03 m.
Using Hooke's law, the spring force (F) can be calculated as F = k * x, where k is the spring constant and x is the displacement from the unstretched position.
Given that the spring constant (k) is 100 N/m and the displacement (x) is 0.03 m, the spring force can be calculated as:
F = 100 N/m * 0.03 m = 3 N
Therefore, the centripetal force on the disc is 3 N. So, the correct answer is (b) 3 N.
Now, to find the work done on the disc by the spring during one full circle, you can use the formula W = F * d, where W is the work done, F is the force, and d is the displacement.
However, in this case, the spring force is acting perpendicular to the displacement. Therefore, the work done by the spring is zero (as the force and displacement are perpendicular). So, the correct answer to the second part is (a) 0 J.
To find the centripetal force on the disc, you will need to use Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement from its equilibrium position.
First, let's calculate the displacement of the spring, which is given as 0.03 m.
Using Hooke's law, we have:
spring force = force constant x displacement
spring force = 100 N/m x 0.03 m
spring force = 3 N
So, the centripetal force on the disc is 3 N, which corresponds to option b) in the multiple-choice options.
Now, onto the second part of the question - the work done on the disc by the spring during one full circle.
As mentioned earlier, the spring always exerts a force perpendicular to the direction of the displacement. In this case, the displacement is in a circular path, while the force from the spring acts radially towards the center of the circle. Therefore, the work done by the spring is zero.
Hence, the correct answer is option a) - 0 J.