Determine the work done by a person when lowering an object of mass 2.6 kg by a distance of 2.4 m. The person applies a force Fext such that the object moves with constant speed, i.e., without acceleration?
My ans:
W=F*d
F = ma
But it's saying constant speed so a=0
However, I realized Fext acts opposite to the weight of the object
so F=mg
and then I can use that value.
Is this correct? Or am I applying the wrong idea
Work=mg*d and that is the energy the person absorbs. Work=mg*d is the work gravity does. Amazing, gravity does work on the person's arms, and he feels it.
Ok I got -W
Because I used g=-9.8m/s^2 because it is acting in the opposite direction relative to the vertical y-axis.
Is this correct? What does -W mean though?
Yes, you are on the right track! The work done by a person is equal to the force applied multiplied by the distance the object moves in the direction of the force. However, in this case, since the object is moving with a constant speed (without acceleration), the net force acting on the object must be zero.
When an object is being lowered at a constant speed, the force applied (Fext) by the person is equal in magnitude but opposite in direction to the weight force (F = mg) acting on the object. This is because the person needs to overcome the force of gravity (mg) to maintain the object's constant speed.
So, in this situation, the work done by the person is given by:
W = Fext * d
Substituting Fext = -mg (opposite direction to the weight force) and the given values, we have:
W = (-mg) * d
W = (-2.6 kg * 9.8 m/s^2) * 2.4 m
W ≈ -60.19 J
Note that the negative sign indicates that work is being done against the force of gravity since the object is being lowered.