Work in springs

  • Thread starter TN17
  • Start date
  • #1
47
0

Homework Statement


A ball of mass 1 kg is attached to a spring. The spring is attached to a fixed pivot, P. The spring cannot bend. The ball moves in a circle of radius R in a horizontal plane with a velocity v. The spring is mass-less and the plane is frictionless.

(a) If R = 1.0 m and v = 1.0 m/s, what is the tension in the spring at the point where it attaches to m?

(b) If the relaxed length of the spring is 0.90 m, what is the spring constant k?

(c) If the ball and spring now rotate with v = 2.0 m/s, what is the new radius of the ball's path.

(d) How much work is done on the mass.


Homework Equations



F = mv2/ R
F = kx
W = Fxcos(theta)

The Attempt at a Solution



a)
F= mv2/ R = 1(1)2 / 1 = 1 N

b)
According to Newton's third law, the force ON the string is equal to the force BY the string, so:
F= kx
1 = k(1-0.9)
10 = k

c)
If R' is the new radius, then:
F = mv2/ R'
and
F = kx = k(R' - 0.9)
SO
mv2/ R' = k(R' - 0.9)
1(2)2/ R' = 10(R' - 0.9)
4/R' = 10(R' - 0.9)
4 = 10R'2 - 9R'
0 = 10R'2 - 9R' - 4

Quadratic formula gives me R'= 1.226 m

d)

Work for any circular motion = 0
because x and F are perpendicular to each other, so cos 90 = 0.

Is this correct?

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #3
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,122
160
(a), (b), and (c) look good.

For (d): I am not sure how to interpret this question. While it's true that no work is done while the mass is moving in a circle of fixed radius, there would be work done on it while the radius changes from 1.0 m to 1.23 m.
 
  • #4
47
0
(a), (b), and (c) look good.

For (d): I am not sure how to interpret this question. While it's true that no work is done while the mass is moving in a circle of fixed radius, there would be work done on it while the radius changes from 1.0 m to 1.23 m.

That's true. =\
How would I find the work while the radius changes?
 
  • #5
296
0
The work done on the mass as the spring stretches would be stored as potential energy is the spring. The elastic energy is the spring is proportional to the extention squared.
 
  • #6
1
0
Do you go to MSS?
 
  • #7
10
0
omg, I go to mss too! xD
 

Related Threads on Work in springs

  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
12
Views
2K
  • Last Post
Replies
1
Views
4K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
7
Views
7K
  • Last Post
Replies
7
Views
13K
Replies
13
Views
3K
  • Last Post
Replies
3
Views
7K
Top