Finding Centre of Gravity | Calculating Moments and Work Done

[crpcrpcrp]

Homework Statement

1.Describe how you would find the centre of gravity of a piece of cardboard of irregular shape.

2.The figure represents a tray held horizontally by a glass of water. The tary has a weight of 6N amd supports a drink of weight 3N.The waiter provides a force at P. The tray may pivot about T.(THE DRAWING IS ATTACHED)

(i)Use the information to find the force provided by the waiter at P and the upward force the hand exerts at T.
(ii)The drink is moved along the tray closer to the hand.Is the force needed to keep the tary horizontal now less, greater or the same? Explain your answer.
(iii)How much work is done by the waiter in lifting the tray and drink through a geight of 0.6m?

Homework Equations

Moments=Force X Distance
M=Fd

Work Done=Force X Distance
W=Fd

The Attempt at a Solution

2(i) 40cm X 3N=5cm X PN
120=5P
120/5=P
24=P
(ii)The force is not less (BUT I CAN'T EXPLAIN WHY)
(iii)Work Done=0.6 X 6N=3.6J

 

[Astronuc]

(ii)The force is not less (BUT I CAN'T EXPLAIN WHY)

There is the mass of the tray and the mass of the glass of water. The total mass (and therefore weight) does not change.

When working with static forces and moments, one looks at net force = 0, and net moment = 0.

The change in moment arm changes the distribution of force, but opposing net forces must add to zero.

 

[PhanthomJay]

The dimensions don't add correctly on your diagram; is the water glass 25 cm from the pivot and is the tray length 40 cm?? Once this is corrected, sum torques about the pivot as you have done, but don't forget to include the torque of the tray weight about the pivot point. You'll need to do a little math to calculate the lever arn length from the tray's center of gravity. And show how to determine the force T. And which force do you use when determining the work done by the waiter in lifting the tray?

 

[crpcrpcrp]

So are my other answers correct? And do you know how would i find the centre of gravity for the irregular shaped piece of cardboard?

 

[PhanthomJay]

So are my other answers correct? And do you know how would i find the centre of gravity for the irregular shaped piece of cardboard?

For the irregular shape, I assume you are trying to find the c.g. experimentally. What is the definition of center of gravity?

For problem 2(i), assuming you have corrected your equation to solve for P, the downward force of the waiter's thumb on the tray, you have not yet shown your attempt to calculate T, the upward force exerted by his fingers.
For (ii), as pointed out, the P and T forces will change, but their sum will not.

For part(iii), the work done by the waiter is the work done against gravity. What is the work done by gravity? Your answer is not correct. Alternatively, you could sum the work done by P and T and get the same result. Show your attempt, please.