Ice in a bowl - work done by gravity

[mybrohshi5]

Homework Statement

An large metal bowl, shaped like a hemisphere, is at rest on a table. The diameter of the bowl is 1.60 m. A mischeivous young man decides to play with a 0.865 kg chunk of dry ice. He releases the chunk of dry ice on the inside upper lip of the bowl; the ice proceeds to slide back and forth in the bowl as if it were a pendulum swinging back and forth at the end of a string. The young man observes that friction between the dry ice and the metal bowl is very small, because the ice returns almost to its release point at the end of every trip across the bowl and back.

calculate the total work done on the sliding ice by gravity from the lowest to the highest point on the path

Homework Equations

W=Fd

The Attempt at a Solution

I thought at first it was just 0J but its not because its only going from the bottom of the bowl to the top so gravity will do work on it to stop the ice at the top and send it back down the bowl.

W=Fd

F is just m(g) = 0.865*9.8 = 8.477N

d is the circumference of half of the bowl

c = 2pi(r)
c= 5.0265
1/2c = 2.5133

W = 8.477(2.5133) = 21.31 J

Can anyone see where i went wrong with this?

Thank you

 

[mgb_phys]

Hint - the work done is the same as just dropping the ice from the height of the top of the bowl down to the bottom.

 

[abbey0]

I solved this one by using the radius instead of the diameter.
Try W=(.865kg)(-9.8)(1.6m/2)

 

[mybrohshi5]

Thats what i was thinking and that is correct but i don't get why.

I don't see how the distance the ice travels is just the radius?

shouldnt the distance it travels be 1/4 (not a half like i was thinking) of the circumference since the ice travels a distance of 1/4 of the bowl?

 

[abbey0]

From what I understand, the distance in the direction of the force is all that matters. In this case, that is in the x direction, which is the radius.

 

[mybrohshi5]

Thanks :)