Why does plastic container slides off at the same speed?

[gijungkim]

Homework Statement

Two small cylindrical plastic containers with flat bottoms are placed on a turntable that has a smooth flat surface. Canister A is empty; canister B contains lead shot. Each canister is the same distance r from the center. The coefficient of static friction between the canisters and the turntable is Us . When the speed of the turntable is gradually increased,

a. only the lighter container slides outward off the turntable; the heavier one stays on.

b. only the heavier container slides outward off the turntable; the lighter one stays on.

c. both containers slide off the turntable at the same turntable speed.

d. the lighter container slides inward.

e. the heavier container slides inward.

Homework Equations

The Attempt at a Solution

The answer is c, but I don't understand why. Can anyone explain it with equations??

 

[Quantum Defect]

Homework Statement

Two small cylindrical plastic containers with flat bottoms are placed on a turntable that has a smooth flat surface. Canister A is empty; canister B contains lead shot. Each canister is the same distance r from the center. The coefficient of static friction between the canisters and the turntable is Us . When the speed of the turntable is gradually increased,

a. only the lighter container slides outward off the turntable; the heavier one stays on.

b. only the heavier container slides outward off the turntable; the lighter one stays on.

c. both containers slide off the turntable at the same turntable speed.

d. the lighter container slides inward.

e. the heavier container slides inward.

Homework Equations

The Attempt at a Solution

The answer is c, but I don't understand why. Can anyone explain it with equations??

Initially, the two containers follow the turntable, correct?

That means that they are undergoing circular motion, which is an acceleration, correct?

The only way that this can happen is if there is a centripetal force pushing in.

What is the force for the two canisters? F= ma. a = v^2/r

The cans fall off when the frictional force becomes less than the centripetal force.

Write two equations for the two cans, and see how the two velocities compare to each other.

 

[gijungkim]

Initially, the two containers follow the turntable, correct?

That means that they are undergoing circular motion, which is an acceleration, correct?

The only way that this can happen is if there is a centripetal force pushing in.

What is the force for the two canisters? F= ma. a = v^2/r

The cans fall off when the frictional force becomes less than the centripetal force.

Write two equations for the two cans, and see how the two velocities compare to each other.

so Us*Fn < mv^2 / r this is when the container slides off right? And if I simplify this equation, I get Us * g = v^2 / r. Since there is no m in this equation, mass doesn't matter right? I don't know if I did it right or not haha

 

[Dick]

so Us*Fn < mv^2 / r this is when the container slides off right? And if I simplify this equation, I get Us * g = v^2 / r. Since there is no m in this equation, mass doesn't matter right? I don't know if I did it right or not haha

Sure it's right. The mass doesn't matter. The 'centripetal force' is proportional to mass and so is the normal force.

 

[gijungkim]

Sure it's right. The mass doesn't matter. The 'centripetal force' is proportional to mass and so is the normal force.

Thank you! :)