Was He Lying?

Classical Mechanics Level 1

Juan and Pedro were both at the circus. Juan told Pedro beforehand that he (Juan himself) actually weighs 512 N. Pedro, who was an engineering student, was quite suspicious, so he asked Juan to ride the Ferris wheel, and took with him a fully-functional weighing scale as well.

As the wheel has almost completed its first cycle, and Juan and Pedro's cabin was near the bottom of the wheel, Pedro asked Juan to stand on the weighing scale. At the exact moment that their cabin was at the bottom part, Pedro measured his friend's weight as exactly 512 N.

Did Juan lie to Pedro when he told him before the ride that he weighs 512 N?

Details and Assumptions
- Their cabin was moving at a constant speed.
- The weighing scale used was unbiased, accurate, and precise.
- Treat Juan and Pedro as point masses.
- The situation was ideal, and all other factors other than gravity such as air, friction, etc., are neglected.

Image credit: Wikipedia

Yes, Juan was lying. No, Juan was not lying. Yes or No, depending on the situation. There is insufficient data for the problem.

10 solutions

Laxman Selvam
Mar 11, 2014

In a vertical circular motion (considering a point mass tied to a string) the maximum tension in the string occurs at the bottom and it is given as T(bottom) = (Mg) +((Mv2)/r). Considering the ferris wheel case, this 'T' is actually the normal force acting on Juan which is the addition of his actual weight and the centrifugal force and that comes out to be 512N. since centrifugal force cannot be zero as long as there is circular motion, Mg must be less than Tbottom. Hence juan's weight is less than 512N. Juan, you have been caught!

I am completely against of this problem. Weight is not an absolute quantity and can vary depending upon the situation. Problem does not say "what is his weight on earth?".

Snehal Shekatkar - 7 years, 3 months ago

Aren't you all assuming this was on earth? On Jupiter there some springs inside the weighing machine could have been broken. They don't clearly state, before boarding the Ferris wheel the weight was zero :-P

Anand Jeyahar - 7 years, 3 months ago

Yes.. I agree.. I have commented on this.. and I think staff will look into the problem again!

Snehal Shekatkar - 7 years, 3 months ago

Repost: But there is no such thing called centrifugal.I recall the words of a text book. Feelings cannot be forces.The feeling of outward push is inertial.The only force acting on the man in the cabin is inward force or centipetal force.So the actual weight of the man is greater than 512.

KRANTHI KIRAN KONDAPALLI - 7 years, 2 months ago

Actually, although centrifugal forces don't naturally exist, they are just as valid as centripetal forces physically. Centripetal forces don't naturally exist either, as they are a proxy term for forces such as gravity and tension. If you choose the earth as the frame of reference, you will detect centripetal force in an astronaut orbiting Earth. If you choose the astronaut as the frame of reference, though, you will detect both centripetal and centrifugal force. It does, in fact, exist, but it is zero in an inertial reference frame.

Edit: it is still valid reasoning to say he weighs more, but it is not because there is no centrifugal force; but in any frame of reference, the centripetal force outweighs the centrifugal force.

Caleb Townsend - 6 years, 2 months ago

centrifugal force is just a short way of explaining the force felt from your inertia and the change in direction

conch shell chemist - 1 year, 11 months ago

it is given that their cabin was moving with constant velocity so how can we concider forces

Saksham Agrawal - 7 years, 3 months ago

No, it was moving at constant speed (i.e. uniform circular motion). So the velocity kept on changing (although the magnitude of the velocity remained constant, direction was changing).

r meh - 7 years, 3 months ago

It is constant speed in circular motion velocity is a variable

Krishna Das - 7 years, 3 months ago

I dont think that the answer to this question given by brilliant is correct(ie, he was lying). As weight is not an quantity which is constant it may vary, when he was on circular path his weight was 512N but when he's in rest with respect to earth his weight would be less, but none of the weight is false weight. So in my views answer is, yes or no depending on the situation is correct answer. I hope brilliant staff would consider this!

Jayank Mayukh - 7 years, 2 months ago

Sunil Swain
Mar 12, 2014

on the wheel, the wieght showed as 512N is the apparent wieght of Juan. The normal force acting on Juan is what recorded in the wieghing machine. In a circular motion( uniform,in this case) the object always needs a centripetal force to stay in a circular path. now here at the bottommost point the force equation appears as[ N-Mg= (Mv^2)/r] Hence his actual wieght must be less than what is being shown.

Trevor B.
Mar 11, 2014

Centrifugal force is adding more force to the weighing, so Juan actually weighs less than $512$ N.

Think about centrifugal force like this. If you pick up an object (like a baseball bat) and spin around holding it in both hands with your arms outstretched, it's going to feel like something is pulling you away from where you are spinning. This is centrifugal force. The momentum of the spinning is pulling you off center, so you are "pulled" away from the center. Similarly, in this situation, the centrifugal force caused by the Ferris wheel rotating is causing Juan to be exerting more downward force than he would if he was just standing up.

It is centrifugal reaction not force centrifugal force is a fictious force this happens when newtons laws are applied in a non inertial frame

Krishna Das - 7 years, 3 months ago

But there is no such thing called centrifugal.I recall the words of a text book. Feelings cannot be forces.The feeling of outward push is inertial.The only force acting on the man in the cabin is inward force or centipetal force.So the actual weight of the man is greater than 512.

KRANTHI KIRAN KONDAPALLI - 7 years, 2 months ago

Chaitanya Pusuluri
Mar 6, 2014

Have to consider the centrifugal force. That adds to the weight as the cabin is at the lowest position.

but the same force also acts on weighing machine so it doesnot make a difference,the weighing machine is not attached to the cabin

Vrks Sai - 7 years, 3 months ago

yes because cars are not eaqul each other

Raja Ali - 7 years, 3 months ago

Centrifugal force

milind prabhu - 7 years, 3 months ago

Brian Traub
Apr 2, 2014

When an object is undergoing circular motion, the centripetal force is acting on the object towards the center of the circle, preventing the object from flying off in any direction. Because this Fc is present, Juan's weight can't be 512 N.

Vamsi Yerraguravagari
Mar 25, 2014

weighing scale measures the net force acting on it which are his weight and the centrifugal force.so we have weight + centrifugal force= 512N.so weight is less than 512.so he is lying

Shakthi Janardhanan
Mar 13, 2014

This is simple.. When u are in a lift or elevator or a ferris wheel , and u are moving down.. u feel lighter,.. this is coz of APPARENT WEIGHT LOSS .. Here, Resultant weight , R is not equal to Mg .. It is given by R = M ( g + a ) , where a is the acceleration of the lift or elevator or whatever it is ... so if Juan says it is 512 N earlier it means he is lying .. Coz it shud be lesser than 512N ..
That's all folks.. :-) :-)

Mahesh Kumar
Mar 11, 2014

T=mg+mv^2/r=512N so mg=512N-mv^2/r so his weight must be less than 512N

William Zhang
Mar 11, 2014

Consider this: when you are in an elevator, your body feels heavier or lighter when the elevator is moving. Similarly, there is a different amount of force acting on the scale when the cabin is moving.

Saqib Ahmed
Mar 11, 2014

Juan weighs less than 512 N because the motion of the ride increases the g force increasing the weight he is lying

Was He Lying?

Image credit: Wikipedia

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