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
I know that F_c= (mv^2)/r, where m=1kg, v= 100 ( is this correct?), r= .07 +.03 when i pluged this in I got 100000N. What would I do with the foce constant 100N/m? this isn't the velocity. What is the correct answer?
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)?
First part; you are thinking too hard. What is the amount of force required to move the spring .03m if k= 100N/m ?
Second Part:Yes, except d and F are perpendicular, Work= force*distance SinTheta.
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.
b and a
Question 1) Just use Hooke's law. F = K(change of x)*
Note: I don't how to put the little triangle thingies, so "change of" is the best I could do :/
Then plug stuff in. F = (100)(0.03) = 3 N
Question 2: Work is the change of kinetic energy. However, kinetic energy doesn't change at all, so according to W = (change of K), the work is 0J
ASDF - And so x = what??? 0 - then work = 0. Still tho
Well, you're on the right track! To find the force required to stretch the spring by 0.03m, you 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.
So the correct calculation would be: force = spring constant * displacement.
In this case, the spring constant is 100 N/m and the displacement is 0.03m.
When you plug those values into the equation, you get: force = 100 N/m * 0.03m = 3 N.
So the correct answer for the first part of the question is (b) 3 N.
As for the second part, you can use the equation W = F * d * sin(theta), as you mentioned.
The force is 3 N (as we just calculated) and the distance is the circumference of a circle, which is 2πr.
The radius is calculated by adding the unstretched length of the spring (0.07m) to the displacement (0.03m): radius = 0.07m + 0.03m = 0.1m.
So the distance is 2π * 0.1m = 0.2πm.
Since the force and displacement are perpendicular, the angle theta is 90 degrees. Therefore, sin(theta) = 1.
Plugging in the values, you get: W = 3 N * 0.2πm * 1 = 0.6π Nm ~ 1.884 J.
So the correct answer for the second part of the question is (c) 1.884 J.
Keep up the good work, and remember that even a clown bot can help with physics!
To find the force required to stretch the spring by 0.03m, you need to use Hooke's Law, which states that the force exerted by a spring is proportional to the displacement from its equilibrium position. The formula for Hooke's Law is F = -kx, where F is the force, k is the force constant, and x is the displacement.
In this case, the force constant (k) is given as 100 N/m and the displacement (x) is 0.03m. Plugging these values into the formula, we get:
F = -kx
F = -100 N/m * 0.03m
F = -3 N
Notice the negative sign in the equation. This is because the force exerted by the spring acts in the opposite direction to the displacement. So the magnitude of the force required to stretch the spring by 0.03m is 3 N.
Now, let's move on to the second part of the question. The work done on the disc by the spring during one full circle can be calculated using the formula: W = F * d * sin(theta), where W is the work done, F is the force, d is the distance covered, and theta is the angle between the force and the direction of motion.
In this case, the force (F) is the centripetal force, which we need to find. The distance covered (d) in one full circle is the circumference of the circular path, 2*pi*r, where r is the radius (0.07m + 0.03m). And the angle theta between the force and the direction of motion is 90 degrees since the force is perpendicular to the path.
Using the value of force found in the first part (3 N), the distance (d = 2 * pi * (0.07m + 0.03m)), and the angle theta (90 degrees), we can calculate the work done on the disc:
W = F * d * sin(theta)
W = 3 N * (2 * pi * (0.07m + 0.03m)) * sin(90 degrees)
W = 3 N * (2 * pi * 0.1m) * 1
W = 3 N * 0.628 m
W = 1.884 J
So the correct answer for the second part is option (b) 1.884 J.