Name(s) ___________________________________________________________ Hr. ___
Practice with 2D tensional forces. Thanks to Mr. Kuhlman for taking these pics.
I am holding up the 19.6 Newton (2 kg) (W = mg, W= 2 kg·9.8 m/s/s = 19.6 Newtons)
weight using TWO strings. The strings are attached to spring scales in different
configurations. You will determine what the spring scales SHOULD READ.
Configuration 1. I am holding the spring scales vertically. This
would be a 1 Dimensional problem.
(a) Draw a force diagram to help you.
(b) Develop a force equation using Fnet = ma (a = 0)
Remember that only upward forces can support the downward
weight.
(c) Solve for the tension (reading on the spring scale).
Each spring scale should say: _____________________ Newtons
(answer: Each spring scale should read 9.8 Newtons as each holds up half of the weight).
2D tensional practice problems, p. 1
Configuration 2. I am holding the spring scales now with thetas (as referenced from the
horizontal) BOTH equal to 75 degrees.
(a) Draw a force diagram to help you (You just need T here, no T1 and T2 as the angle is
the same on both sides).
(b) Develop a force equation using Fnet = ma (a = 0). Remember that only upward forces
can support the downward weight. You’ll need to use sine theta to help you on this one.
.
(c) Solve for the tension (reading on the spring scale).
Each spring scale should say: _____________________ Newtons
(answer: each spring scale should read 10.1 Newtons, now)
2D tensional practice problems, p. 2
Configuration 3. I am holding the spring scales now with thetas (as referenced from the
horizontal) BOTH equal to 50 degrees.
(a) Draw a force diagram to help you. (You just need T here, no T1 and T2 as the angle is
the same on both sides).
(b) Develop a force equation using Fnet = ma (a = 0). Remember that only upward forces
can support the downward weight. (again, use sin theta to help you) .
(c) Solve for the tension (reading on the spring scale).
Each spring scale should say: _____________________ Newtons
How did this reading compare to the reading on the previous page? Did it increase,
decrease, so stay the same?
(answer: each spring scale should read 12.8 Newtons, now, and our tensional readings are increasing as the angle lessens)
2D tensional practice problems, p. 3
Configuration 4. I am holding the spring scales now with thetas (as referenced from the
horizontal) BOTH equal to 30 degrees.
(a) Draw a force diagram to help you. (You just need T here, no T1 and T2 as the angle is
the same on both sides).
(b) Develop a force equation using Fnet = ma (a = 0). Remember that only upward forces
can support the downward weight. (again, use sin theta to help you) .
(c) Solve for the tension (reading on the spring scale).
Each spring scale should say: _____________________ Newtons
So, what is happening to the tension according to the spring scale as our angle gets
smaller?
(answer: each spring scale should read 19.6 Newtons, now, and our tensional readings are increasing as the angle lessens)
2D tensional practice problems, p. 4
Configuration 5. I am holding the spring scales now with thetas (as referenced from the
horizontal) BOTH equal to 0 degrees. I don’t have a picture of this.
(a) Draw a force diagram to help you (I’ve done this one for you)
(b) Develop a force equation using Fnet = ma (a = 0). Remember that only upward forces
can support the downward weight. (again, use sin theta to help you) .
(c) Solve for the tension (reading on the spring scale).
T
T
W
Each spring scale should say: _____________________ Newtons
Do you understand now why I couldn’t take a picture? Why not???
(answer: each spring scale should read infinity (∞) Newtons. When we try to divide by the sine of 0 deg, we get an error on
our calculator. This is because our tension has increased to infinity. This is an impossible situation; no string can support this
much weight. Another way of looking at this is that a vertical force (weight) CANNOT be supported by horizontal forces. I
COULD NOT take a picture as this is an impossible picture to take!)
2D tensional practice problems, p. 5
Configuration 6. I am holding the spring scales now with different thetas (as referenced
from the horizontal) The left theta (call it theta 1 connected to T1) = 35 deg and the right
theta (call it theta 2 connected to T2)= 75 degrees.
(a) Draw a force diagram to help you; you have T1 on left and T2 on the right now.
(b) Develop a force equation using Fnet = ma (a = 0). Remember that only upward forces
can support the downward weight. (use sin theta AND cosine theta to help you).
(c) Solve for the T1 and T2 (reading on the spring scale). You may want to go back to your
notes here. You’ll need to use both the x equation and the y equation.
The left spring scale (T1) should read ___________________ Newtons.
The right spring scale (T2) should read ____________________Newtons.
(answers: T1 = 5.4 Newtons and T2 = 17 Newtons).
2D tensional practice problems, p. 6