I don't understand why this is wrong (Work and kinetic energy problem)

[frankfjf]

Okay, here's the problem:

A cord is used to vertically lower an initially stationary block of mass M = 6.4 kg at a constant downward acceleration of g/2. When the block has fallen a distance d = 4.8 m, find (a) the work done by the cord's force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. (Note : Take the downward direction positive)

For a I come up with the equation:

F - Mg = Mg/2.

Solving for F I get:

F = 3Mg/2

Plugigng this into the basic equation for work I get:

W = 3Mgd/2

But when I plug in my values for M, g, and d, I get a wrong answer. Why?

 

[nrqed]

Okay, here's the problem:

A cord is used to vertically lower an initially stationary block of mass M = 6.4 kg at a constant downward acceleration of g/2. When the block has fallen a distance d = 4.8 m, find (a) the work done by the cord's force on the block, (b) the work done by the gravitational force on the block, (c) the kinetic energy of the block, and (d) the speed of the block. (Note : Take the downward direction positive)

For a I come up with the equation:

F - Mg = Mg/2.

Solving for F I get:

F = 3Mg/2

Plugigng this into the basic equation for work I get:

W = 3Mgd/2

But when I plug in my values for M, g, and d, I get a wrong answer. Why?

If there is a *downward* acceleration of g/2, it means that $a_y = - g/2$. You used +g/2 in your equation.

 

[frankfjf]

But it says to take the downward direction to be positive.

 

[nrqed]

But it says to take the downward direction to be positive.

All right. Then your equation should be -F + Mg = Mg/2

 

[topsquark]

All right. Then your equation should be -F + Mg = Mg/2

And then when you calculate the work done, F is upward and d is downward.

-Dan