Maximum kinetic energy

In summary, the problem involves an object constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16N. The maximum kinetic energy can be found by setting the tension equal to the centripetal force and solving for the velocity. This results in a velocity of 2.21 m/s and a maximum kinetic energy of 4 J. The final solution is 1/2*16*r, where r is the radius of the circular path.
  • #1
hansel13
51
0

Homework Statement


An object is constrained by a cord to move in a circular path of radius 0.5m on a horizontal frictionless surface. The cord will break if its tension exceeds 16 N. What is the maximum kinetic energy?


Homework Equations


T=mg
KE=1/2mv2



The Attempt at a Solution



Really lost on this problem. Am I applying the wrong formulas?
 
Physics news on Phys.org
  • #2
if its moving in a circular horizontal path the tension isn't mg its equal to the centripetal force (mv2/r)

so I am guessing you set the centripetal force to equal 16 to solve for v. After that you can find the KE
 
  • #3
thanks teckid.

So a = v2/R

so V = (a*R)1/2
V = (9.8*.5)1/2
V = 2.21

T=(mv2)/R
m = T*R/(v2)
m = 1.63

So for KE, we have:
KE = 1/2*m*v2
KE = 1/2*1.63*2.212
KE = 4 J

I think that's right..
 
  • #4
No i think you're confusing horizontal and vertical... vertical suggest there is a downward force due to gravity (aka 9.81...). However, here the path is horizontal, like a merry-go-round, so there gravity does not effect the tension on a frictionless surface. since the tension must be 16 or less and the tension is equal to the centripetal force then:

16 = mv2/r

further...

16 *radius * mass = v2
(16*radius*mass).5 = v

with this velocity you can find the max KE (.5MV2)

You should not be using centripetal acceleration to find the velocity unless we know what that acceleration is.
 
  • #5
(16*radius*mass)^.5 = v

But this leaves us with 2 unknown variables (mass and velocity)...
 
  • #6
Not really.

Maximum F = mv²/r = 16N

But Kinetic Energy is ½mv²

But you know that mv² = 16*r

Which means your KE is merely ½*16*r
 

What is maximum kinetic energy?

Maximum kinetic energy is the maximum amount of energy that an object has while in motion. It is a measure of the object's speed and mass.

How is maximum kinetic energy calculated?

The formula for calculating maximum kinetic energy is KE = 1/2 * m * v2, where m is the mass of the object and v is its velocity.

What factors affect maximum kinetic energy?

The two main factors that affect maximum kinetic energy are the mass and velocity of the object. As the mass or velocity increases, the maximum kinetic energy also increases.

Can maximum kinetic energy be negative?

No, maximum kinetic energy cannot be negative. It is always a positive value, as it represents the maximum amount of energy an object has while in motion.

How is maximum kinetic energy different from momentum?

Maximum kinetic energy and momentum are two different concepts. Maximum kinetic energy is a measure of the object's energy while in motion, while momentum is a measure of the object's motion or tendency to keep moving. Maximum kinetic energy depends on both the speed and mass of the object, while momentum only depends on the mass and velocity of the object.

Similar threads

  • Introductory Physics Homework Help
Replies
9
Views
707
  • Introductory Physics Homework Help
Replies
33
Views
815
  • Introductory Physics Homework Help
Replies
2
Views
755
  • Introductory Physics Homework Help
Replies
2
Views
4K
  • Introductory Physics Homework Help
Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
9
Views
1K
  • Introductory Physics Homework Help
Replies
7
Views
1K
  • Introductory Physics Homework Help
Replies
6
Views
1K
  • Introductory Physics Homework Help
Replies
10
Views
2K
Back
Top