Energy related problem

  • Thread starter vbtweakin
  • Start date
  • #1
3
0
the problem states as this
it's a energy related problem

A sled starts from rest at the top of the frictionless, hemispherical snow-covered hill.
a)Find an expression for the sled's speed when it is at angle "theta"
b)Use Newton's laws to find the maximum speed the sled can have at angle "theta" without leaving the surface.
c)at what angle "theta"max does the sled "fly off" the hill?

since the surface is fristionless the energy is conserved we can say E at start = E at angle theta
now i realize at the top the sled has zero kinetic energy and Pe=mgR
and the at point "thete" Ke=1/2mV^2 and Pe=mgh

now at this point im stuck and not sure what to do with all this data

thanks in advance
 

Attachments

  • picture.jpg
    picture.jpg
    2.4 KB · Views: 424

Answers and Replies

  • #2
Galileo
Science Advisor
Homework Helper
1,989
6
Since only gravity is doing work, the potential energy of the sled is converted to kinetic energy.
Try to find the height of the sled as a function of theta.
 
  • #3
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
134
Also remember that only gravity can provide the necessary centripetal acceleration..
 
  • #4
Doc Al
Mentor
45,084
1,394
Don't forget to use Newton's 2nd law to analyze the forces on the sled. Since it follows a circular path (until it leaves the surface), apply what you know about centripetal acceleration.
 
  • #5
3
0
would the height be equal to h=r sin(theta)?
 
  • #6
3
0
well considering centripedal forces i have
a=V^2/rsin theta
Fn-mg=ma
Fn-mg=mV^2/R sin theta
Fn=mg-mV^2/R sin theta
0=mg-mV^2/R sin theta
mV^2=mgRsin theta
V= sqrt(g Rsin theta)
 
  • #7
arildno
Science Advisor
Homework Helper
Gold Member
Dearly Missed
9,970
134
vbtweakin said:
would the height be equal to h=r sin(theta)?
The angle is measured with respect to the vertical (in your diagram), so your height should have maximum value when the angle is zero. Does the sine function give you that?
 

Related Threads on Energy related problem

  • Last Post
Replies
5
Views
8K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
8
Views
6K
Replies
2
Views
2K
Replies
2
Views
4K
Replies
13
Views
5K
Replies
0
Views
2K
  • Last Post
Replies
1
Views
491
Replies
1
Views
4K
Replies
15
Views
409
Top