Retarding force solve for v

  • Thread starter carlee172
  • Start date
  • #1
8
0

Homework Statement



A rock with mass m slides with initial velocity vo on a horizontal surface. A retarding force FR that the surface exerts on the rock is proportional to the square root of the instantaneous velocity of the rock FR=-kv1/2.
A) Find expression for the velocity of the rock as a function of time.
Express your answer in terms of the variables m, vo, k, and t.

Homework Equations



F=ma

v=vo +at

etc..

The Attempt at a Solution



vbasically included solving and substituting F=ma, FR=-kv1/2 and v=vo +at
in the end i got v=vo -kv1/2t/m

obviouslt this isnt right because i have v on both sides of the equation.. help
 

Answers and Replies

  • #2
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,102
130
Welcome to PF.

v=vo +at doesn't work here, because you need a constant acceleration for that equation.

F=ma is a good start. You'll also need to use some calculus to solve this one.
 
  • #3
8
0
ok, so:

-k[tex]\sqrt{}v[/tex]=m(dv/dt)
then integrate the first side from 0 to t and the left side from vo to v
and then solve for v, i got:
v=((-kt-2(v1/2)m)/2m)2
 
  • #4
8
0
ok so i got the answer v=(4m2v0-4ktmv1/2+k2t2)/4m2
now, i have to find the integral (distance). for t, the rest are constants i guess
 
  • #5
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
12,102
130
One problem with that expression is that it's supposed to be an expression for v in terms of t and the other variables, i.e. given t, m, k, and v0, you should be able to calculate v.

But you have v there on the right-hand-side, so it's not really an equation for v.

ok, so:

-k[tex]\sqrt{}v[/tex]=m(dv/dt)
Let's go back to this equation. I didn't really follow what you did after that, but I would separate the two variables, v and t, before integrating. I.e., put all the v's (including the dv term) on one side of the equation, and put dt on the other side. Then integrate.
 

Related Threads on Retarding force solve for v

  • Last Post
Replies
2
Views
7K
  • Last Post
Replies
10
Views
643
Replies
7
Views
4K
  • Last Post
Replies
1
Views
6K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
4
Views
8K
  • Last Post
Replies
7
Views
25K
Replies
9
Views
733
Top