# Max Kinetic Energy of Object in Circular Path with Constraint

• tprofl
In summary, an object constrained to move in a circular path of radius 0.5m on a horizontal frictionless surface has a maximum kinetic energy of 16J before the cord will break. This is determined by considering the centripetal force required for circular motion and the relationship between kinetic and potential energy.
tprofl

## 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 tension exceeds 16N. The maximum kinetic energy the object can have is:

KE=1/2mv^2
U=mgh

## The Attempt at a Solution

Because the object is spinning in a horizontal circle, you may take the tension at any point. Potential can equal kinetic, mgh=1/2mv^2, but I can't figure out how to start this problem.

Welcome to PF!

tprofl said:

## 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 tension exceeds 16N. The maximum kinetic energy the object can have is:

KE=1/2mv^2
U=mgh

## The Attempt at a Solution

Because the object is spinning in a horizontal circle, you may take the tension at any point. Potential can equal kinetic, mgh=1/2mv^2, but I can't figure out how to start this problem.

I can't figure out what you're saying in your solution attempt, in particular, the bit about taking the tension "at any point."

Furthermore, since the circle is horizontal, the object never changes height, meaning that its gravitational potential energy is constant. Potential energy, therefore, is somewhat irrelevant to the problem.

Try, instead, to think of it this way: since kinetic energy depends on speed, the object's maximum kinetic energy is going to depend on its maximum possible speed. What determines the speed of an object in uniform circular motion? Hint: what kind of force is the tension in the rope providing in order to produce circular motion?

tprofl said:

## 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 tension exceeds 16N. The maximum kinetic energy the object can have is:

KE=1/2mv^2
U=mgh

## The Attempt at a Solution

Because the object is spinning in a horizontal circle, you may take the tension at any point. Potential can equal kinetic, mgh=1/2mv^2, but I can't figure out how to start this problem.

Because this object is on a horizontal table, its gravitational potential energy (mgh) doesn't ever change.

The centripetal force required to keep an object in circular motion is given by mv2/R

I was always interested in comparing the kinetic energy formula 1/2 mv2 as they both contain the mv2 expression

By comparing and combining those two expressions/formulas I think you can discover the answer you seek.

## 1. What is the formula for calculating the maximum kinetic energy of an object in a circular path with a constraint?

The formula for calculating the maximum kinetic energy of an object in a circular path with a constraint is KE(max) = (1/2)mv2, where m is the mass of the object and v is its velocity.

## 2. How does the constraint affect the maximum kinetic energy of the object in a circular path?

The constraint, such as a rope or a string, limits the distance the object can travel from its center of rotation. This results in a smaller radius, which in turn decreases the maximum kinetic energy of the object.

## 3. Can the maximum kinetic energy of an object in a circular path with a constraint ever be greater than the kinetic energy of the same object in an unconstrained circular path?

No, the maximum kinetic energy of an object in a circular path with a constraint can never be greater than the kinetic energy of the same object in an unconstrained circular path. The constraint limits the distance the object can travel, resulting in a smaller radius and therefore, a lower maximum kinetic energy.

## 4. How does the mass of the object affect the maximum kinetic energy in a circular path with a constraint?

The mass of the object directly affects the maximum kinetic energy in a circular path with a constraint. The greater the mass, the greater the maximum kinetic energy will be, as seen in the formula KE(max) = (1/2)mv2.

## 5. Can the maximum kinetic energy of an object in a circular path with a constraint be zero?

Yes, the maximum kinetic energy of an object in a circular path with a constraint can be zero if the object is not moving. This can happen if there is no initial velocity or if the object has come to a complete stop due to external forces.

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