Conservation of Energy: Finding the Speed of a Falling Ball

AI Thread Summary
The discussion revolves around calculating the speed of a falling ball using the conservation of energy principle. The initial equation set up is m2gh - fh = 1/2(m1 + m2)v^2, where m2 is the mass of the falling ball, m1 is the mass on the surface, and fh represents the frictional force. The calculations yield a speed of 4.77 m/s, which does not match the expected answer. Participants are encouraged to reconsider the signs in their equations, particularly regarding the frictional force. The conversation emphasizes the importance of correctly applying the conservation of energy concept in solving the problem.
sireh
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Homework Statement


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The coefficient of friction between the block of mass m1 = 3.00kg and the surface in Figure P7.22 is μk = 0.400. The system starts from rest. What is the speed of the ball of mass m2 = 5.00 kg when it has fallen a distance of h = 1.50m?

Homework Equations


This is in the chapter on conservation of energy, so
Ui + Ki + ΔEmech = Uf + Kf

The Attempt at a Solution


Using downward direction as positive so g is positive

m2gh - fh = 1/2(m1 + m2)v2
(5.00kg)(9.8m/s2)(1.5m) - (-11.76N)(1.5m) = 1/2(3.00kg + 5.00kg)v2
91.14Nm = 4kg * v2
22.785Nm2/s2 = v2
4.77m/s = v

That's not the answer that I'm seeing on the answer sheet. I'm not sure what I did wrong.
 
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sireh said:
m2gh - fh = 1/2(m1 + m2)v2
(5.00kg)(9.8m/s2)(1.5m) - (-11.76N)(1.5m) = 1/2(3.00kg + 5.00kg)v2
Think conceptually and decide if you want to have two minus signs here.
 

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