No Work Done during Circular Motion

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In circular motion, work done is calculated using the formula Work Done = Force x Distance x cos(Theta), where Theta is the angle between the force and displacement vector. Since the force acting on an object in circular motion is always directed towards the center, it is perpendicular to the displacement vector. This means that the angle Theta is 90 degrees, resulting in cos(90°) = 0, indicating that no work is done. The discussion emphasizes that the velocity in circular motion does not contribute to work since the direction of displacement is consistently perpendicular to the force. Therefore, it is concluded that no work is done during circular motion.
Peter G.
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Hi guys, :smile:

Work Done = Force x Distance x cos of Theta - the angle between the Force and the Displacement Vector / direction of motion

In Circular motion I know the force but I am given velocity. In order to prove that no work is done is it correct to say the following:

If we have two velocities, one horizontal and another vertical and find the resultant, the direction of the resultant velocity will be the direction of the displacement vector.

Hence, in circular motion, we only have one velocity vector, we don't need to add. We can then consider it to be the direction of the displacement vector - this would always be at 90 degrees to the force making me understand that no work is done.

Thanks,
Peter G.
 
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Ok, so I will try and make my point clearer: Check the attachment.
 

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The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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