Early one October you go to a pumpkin patch to select your Halloween pumpkin. You lift the 2.6 kg pumpkin to a height of 1.08 m, then carry it 51.5 m (on level ground) to the check-out stand.
(a) Calculate the work you do on the pumpkin as you lift it from the ground.

(b) How much work do you do on the pumpkin as you carry it from the field?




I know that the answer to part a is 27.55 J by W=Fd
W=m*g*d
W= (2.6 kg)(9.81 m/s^2)(1.08 m) = 27.55 J

I am having trouble finding the right answer to the second part of the question. I have tried a few combinations but nothing is giving me a correct answer.
I tried W=(2.6 kg)(9.81)(51.55m) = 1313.559 J
I added this to the answer from part a for total work on the pumpkin = 1341.109 J
I tried W=F(cos(0))d. = 9.81(cos(0))51.5 = 505.215 J
It just doesn't seem like it should be that difficult. What am I missing?

Is it not simply 1313.559 J as you got it?

I mean, only W=Fd, and no more, because if you held a pumpkin above the ground and don't move, it is not considered work. So, only the distance travelled is considered. Were you given the answer?

Remember that work is actually a scalar quantity defined as the Force acting over a distance :



This is a fancy way of saying that work is Force times Distance times the cosine of the angle between them. As you carry the pumpkin the force due to gravity is in the direction down towards the ground, but the distance you travel is horizintal to the ground. Therefore the force and distance vectors are perpendicular to each other, and hence you do no work on the pumpkin as you carry it.