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

Pendulum angle problem

  • #1

Homework Statement


1) A pendulum consists of a 2 kg stone swinging on a 4 m long string
of negligible mass. The stone has a speed of 8 m/s when it passes its
lowest point. a) What is the speed of the rock when it is at an angle of
60 degrees to the vertical? b) What is the greatest angle with the vertical
that the string will make during the stone's motion?


Homework Equations


Not really sure Just trying to do it with energy conservation..


The Attempt at a Solution



Well I figured out that at 60 degree's the height of the stone from the ground is 2m

Thne I figured I should use E = k+mgy ...
and came up with Einitial = (1/2)(2kg)(8m/s)^2 + (2kg)(-9.8m/s^2)(4m)

Efinal = (1/2)(2kg)(v)^2 + (2kg)(-9.8m/s^2)(2m)


Where to go Next... no clue
 

Answers and Replies

  • #2
Dick
Science Advisor
Homework Helper
26,258
618
"energy conservation". Set Einitial=Efinal and solve for v.
 
  • #3
Dick
Science Advisor
Homework Helper
26,258
618
Be careful about the sign and stuff on your gravitational terms though. It's mgh, where h is the height above the ground and there is no minus sign on the g.
 
  • #4
"energy conservation". Set Einitial=Efinal and solve for v.
Really... can you tell me what that is derived from like ive seen deltaE = E final - E initial..
 
  • #5
Dick
Science Advisor
Homework Helper
26,258
618
Really... can you tell me what that is derived from like ive seen deltaE = E final - E initial..
There's no energy going into or out of the system. So deltaE=0. Right?
 
  • #6
Im getting v @ 60 degrees = sqrt(55.2) You?
 
  • #7
Okay for part B im going to assume that Einitial will remain the same... But Efinal will be = 0 + (2kg)(9.8m/s^2)(4m(1-cos(theta))
 
  • #8
Then again Im assuming I can set them equal to each other.. cause no energy is gained or lost. so That gives me 94.4 = (2kg)(9.8m/s^2)(4m(1-cos(theta))

94.4 = 19.6(4m(1-cos(theta))

94.4 = 78.4(1-cos(theta))

.204081633 = -cos(theta)

-.204081633 = cos(theta)

cos^(-1)(-.2040816330) = theta
 
  • #9
im getting (theta) = 101.775744 degrees

101.8 Degrees
 
  • #10
Dick
Science Advisor
Homework Helper
26,258
618
Im getting v @ 60 degrees = sqrt(55.2) You?
Sorry. No, I don't get that. Can you post details? And you didn't post part B either. So I don't know what you are working on.
 

Related Threads on Pendulum angle problem

  • Last Post
Replies
5
Views
12K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
16
Views
1K
  • Last Post
Replies
13
Views
1K
  • Last Post
Replies
3
Views
2K
  • Last Post
Replies
0
Views
2K
  • Last Post
Replies
12
Views
17K
Top