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Concept of Work (j direction) at constant acceleration watch

1. Help would be appreciated

A cord is used to lower vertically a block of mass M a distance d at a constant downward acceleration g/4.
(i) Find work done by cord on the block, and the work done by gravity.
My answer: I drew a force diagram. From it I noted that a tensional force was found to be in the rope.

By Newton II, F=ma (more specifically F is the sum of all forces that would cause the block to accelerate)

The forces are Tension and weight which is equal to ma.

I took down to be negative.

So, T + (-W) = -ma
=> T = 3/4mg

Work done: Work = Fdcos(180)

W = -3/4mg (work done by cord on block)

Work done due to gravity? Surely the same as above?

(ii) Change in kinetic energy

Considering work is the net change in kinetic energy it would be rather simple. But since the body is undergoing constant acceleration, velocity is zero and therefore the change in kinetic energy. Doesn't make sense because the object is moving?

Same as for (i)?

Thanks
2. (Original post by Everybody)
Help would be appreciated

A cord is used to lower vertically a block of mass M a distance d at a constant downward acceleration g/4.
(i) Find work done by cord on the block, and the work done by gravity.
My answer: I drew a force diagram. From it I noted that a tensional force was found to be in the rope.

By Newton II, F=ma (more specifically F is the sum of all forces that would cause the block to accelerate)

The forces are Tension and weight which is equal to ma.

I took down to be negative.

So, T + (-W) = -ma
=> T = 3/4mg

Work done: Work = Fdcos(180)

W = -3/4mg (work done by cord on block)
Almost correct. You're missing displacement in your last equation

Work done due to gravity? Surely the same as above?

(ii) Change in kinetic energy

Considering work is the net change in kinetic energy it would be rather simple. But since the body is undergoing constant acceleration, velocity is zero and therefore the change in kinetic energy. Doesn't make sense because the object is moving?

Same as for (i)?
Firstly, acceleration is constant, not speed. Speed is changing at 9.8/4 m/s per second

Work done by gravitational force would be calculated in the same way as you calculated the work done by the cord. .

The change in kinetic energy is the result of doing the work by gravity and by cord:

.

You could also think about in another way: the body is moving at a constant acceleration of g/4. Therefore there is a net force acting on it of a magnitude of Mg/4. Work done by this net force is Mgd/4.

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