Berkeley Review Physics Section 2 Question 23

[WSK22]

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(Sorry if this is in the wrong spot.)

The question asks: "If a person starts at the rim of a spinning platform and is pushed radially toward the central axis by a moving exterior wall, then what happens to the normal force felt by that person due to the wall?"

Answer reads: "It decreases, since r decreases."

I understand that the centripetal acceleration decreases as r decreases because centripetal acceleration=w^2 x r, but how is it that a decrease in centripetal force causes a decrease in the normal force if both point in the same direction?

If centripetal acceleration, centripetal force, and normal force are all pointing inward then wouldn't the sum of all forces = ma = Fc + Fn; which would mean that Fn = ma-Fc and thus a decrease in Fc would increase Fn? Fc = ac x mass so a decrease in ac means a decrease in Fc which, according to the above calculation, would increase Fn if ma stays constant (in the answer discription is states that the platform spins at a constant speed).

Conceptually, if the centripetal force decreases, and there's less inward force acting on the object, then more force is placed on the wall--which translates to an increase in the normal force (assuming the wall doesn't move backwards). The normal force would have to 'pick up' what the centripetal force lost because they both act in the same direction.

What am I doing wrong?

 

[TheRealAngeleno]

I don't think there is a decrease or change in the centripetal force.

mv^2 / r = Fc + N
mv^2 / r - Fc = N

Since r decreases, centripetal acceleration decreases and so the normal force N would decrease as well while the centripetal force Fc remains constant. Someone please do correct me if I'm wrong.

 

[WSK22]

Maybe. I thought that because Fc=mv^2/r and ac=v^2/r then Fc=(ac)(mass) so if the mass stays constant and the ac decreases then the Fc must decrease too? 😕

 

[Rabolisk]

Centripetal force is the normal force in this situation. Centripetal force is simply the force that acts towards the center. Normal force acts towards the center, so by definition, it is a centripetal force. Any force can serve as the centripetal force; the centripetal part only describes the direction of the force relative to the motion of the object. A centripetal force isn't something in it of itself (like gravity or friction).

I understand that the centripetal acceleration decreases as r decreases because centripetal acceleration=w^2 x r, but how is it that a decrease in centripetal force causes a decrease in the normal force if both point in the same direction?

The first part is true. A decrease in centripetal force is a decrease in normal force, because the two are one and the same.

 

[drechie]

when i approached this problem i thought the normal force was the force perpendicular to the floor of the moving structure and would be equal to mass x gravity. in this problem the normal force is the centripel acceleration - why? and are there "two" normal forces for this problem?