Anonymous
Anonymous asked in Science & MathematicsPhysics · 4 weeks ago

# Physics problem?

When an object is thrown upwards into the air, how does the the work done by gravity compare to the work done by air resistance in terms of their signs? (both positive, both negative, opposite)

The object has come back down to the same level that it was initially released. Compare the work done by gravity to the work done by air resistance. (which are zero, positive, or negative?)

Relevance

Work done by gravity is Q = Fs = Mgh; where W = Mg is the weight of the object of mass M and s = h is the height attained by the tossed object. As the object is being slowed down by gravity's work, the vector of Q is downward in the direction opposite to the upward velocity of the object while it's still ascending.

Since the rate of rise, the velocity, is slowing, due to the work being done by gravity, we can say the object is decelerating as it climbs upward. Another term for deceleration is negative acceleration.

In sum, while the object is ascending, the work Q and the acceleration g, due to gravity are all pointing downward. If you wish you can call that negative. (both negative) Now we look at the drag (aka, air resistance).

Profile drag, caused by the object's shape and velocity through the air, always acts in the direction opposite to the velocity vector. In this case, as the object ascends, the profile drag vector will be downward. And as we chose downward to be negative in the gravity case, we must call it negative here as well.

So both drag and gravity work are negative while ascending. ANS.

After the object reaches zero velocity at its max height H it will fall back to where it came from. Now the weight and the direction of motion are in the same direction...downward. So the gravity work is once again negative...downward. But here's the difference....

The object is now moving downward too; so it's going in the same direction as the work vector. Which means rather than decelerating, the object is now accelerating. So starting from zero velocity at max height, the object is falling faster and faster as it drops from max height.

But profile drag still acts in the direction opposite to the direction of motion...the object is heading downward now; so the drag force is now upward....positive.

So drag and gravity force are acting in opposite directions while falling. And, here's the result, because the object lands with some velocity, the so-called impact velocity, the work done by gravity to accelerate the object exceeded the work down by drag to slow it down. And given that gravity's work was in the direction of fall, that work is positive compared to the drag work which is far less.

Compared to drag while falling, gravity work is positive. ANS.