• Support PF! Buy your school textbooks, materials and every day products Here!

Determining tension

  • Thread starter red123
  • Start date
  • #1
22
0

Homework Statement



The Ball has a mass of 30 kg and a speed v = 4 m/s at the instant it is at its lowest point, θ = 0°. Determine the tension in the cord and the rate at which the ball's speed is decreasing at the instant θ = 20°. Neglect the size of the ball.

245kjfa.jpg


Homework Equations



ΣF = ma
an = v2

The Attempt at a Solution



T = mg + mv2
= 30kg(9.81 m/s2) + 30kg(4 m/s2)
= 414.3 N
 
Last edited:

Answers and Replies

  • #2
rock.freak667
Homework Helper
6,230
31
That looks correct. So onto the second part.
 
  • #3
163
0
I would check the velocity at the point θ = 20º, because as I'm seeing in your attempt you're using the same very velocity as θ = 0º.
 
  • #4
22
0
That looks correct. So onto the second part.
It doesn't agree with my textbook's answer, T = 361 N
 
  • #5
rock.freak667
Homework Helper
6,230
31
It doesn't agree with my textbook's answer, T = 361 N
If that was the case, then v≠4 m/s.
 
  • #6
163
0
Well, yeah the thing is that v = 4m/s at θ = 0º; but it is clear that at θ = 20º the velocity should differ, which should be easily calculated by energy conservation.
 
  • #7
rock.freak667
Homework Helper
6,230
31
Well, yeah the thing is that v = 4m/s at θ = 0º; but it is clear that at θ = 20º the velocity should differ, which should be easily calculated by energy conservation.
If you use the tension given as the answer and work towards a velocity, it will be less than 4.
 
  • #8
163
0
Yeah that's how it should be. For example:

[tex]E_t = mgh + 1/2mv^2[/tex] so, as the h increases according to the angle, the potential will also do so, while the velocity will drop.
 
  • #9
123
1

Homework Equations



an = v2
Your problem occurred right here. Note that the ball is not moving in uniform speed, it drops down before it completes a loop. Therefore, it is not uniform circular motion and this equation does not work over here. Also note that naturally, tension force does not exceed the bigger external force on the bodies. That means at the lowest point, the tension equals to the force of gravity.
Another way of thinking of it is optimization. A graph reaches it's maximum when the slope of the tangent is 0. In a v-t graph, the slopes of tangents are the accelerations of the specific instants. Since the slope of the tangent is 0 at the lowest point, therefore the acceleration is 0. This leads to F_net=0.
 
  • #10
123
1
Try using conservation of energy.

Determine the tension in the cord and the rate at which the ball's speed is decreasing at the instant θ = 20°. Neglect the size of the ball.
Another problem you had was this. you are to find tension and acceleration at 20o
 

Related Threads on Determining tension

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
1
Views
996
  • Last Post
Replies
5
Views
959
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
3
Views
869
Replies
9
Views
12K
  • Last Post
Replies
2
Views
1K
Replies
3
Views
2K
Replies
18
Views
5K
Top