(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w

T is greater

Explanation:

Since the elevator is moving against gravity more work will be done on the rope

T= m(g+a)

T is greater when the elevator is accelerating upwards.

Explanation:

The tension in the cable is given by the formula

T = m(g+a)

Taking upwards as positive, when the elevator is accelerating upwards a is positive and and g+a is greater than g

So the tension is greater than the weight mg.

But when the elevator is accelerating downwards the, the acceleration a is negative and g +a in the equation above is less than g and as a result the Tension force T is less than the weight w.