Questions about course of Energy conservation

[physicos]

Thank you for helping me
1-
One end of a rubber band is tied down and you pull on the other end to trace a complicated closed trajectory.If you were to measyre the elastic force F at every point and took its scalar product with the local displacement F^→*r^→,and then summed all f these . What would you get ?

I said it would give the overall force of F over the whole trajectory on the rubber band : IS IT CORRECT ?

2- How much work do you do when you hold a bag of groceries while standing still (I said : W= m*g*h) with m mass of groceries and h height of the bag from ground.
How much work do you do when you hold the same bag along a distance d across the parking lot of the grocery store(I said W= mg*d )
IS IT CORRECT ?

 

[mfb]

I said it would give the overall force of F over the whole trajectory on the rubber band : IS IT CORRECT ?

What do you mean with "the overall force of F over the whole trajectory"?
No, it is not correct.

2- How much work do you do when you hold a bag of groceries while standing still (I said : W= m*g*h) with m mass of groceries and h height of the bag from ground.

What's so special about the ground here? The problem statement did not say you have to pick it up. You are just holding it.

How much work do you do when you hold the same bag along a distance d across the parking lot of the grocery store(I said W= mg*d )
IS IT CORRECT ?

No. Think about the directions of forces and motion.

 

[physicos]

What do you mean with "the overall force of F over the whole trajectory"?
No, it is not correct.

What's so special about the ground here? The problem statement did not say you have to pick it up. You are just holding it.

No. Think about the directions of forces and motion.

1-I meant with the overall force that F*Δr where just particle of work !
2- I really don't know what is so special ! I've copied the excercise as it is !

 

[mfb]

1-I meant with the overall force that F*Δr where just particle of work !

There is no F*Δr in the problem.

2- I really don't know what is so special ! I've copied the excercise as it is !

Sure, but your answer would imply there is something special about the ground...
How much work does a table need to hold something? If you give a similar answer again, where would the table get such energy from? ;)

 

[HalfLostAndSearching]

1- Yes, your explanation is correct. The scalar product of the elastic force and local displacement at each point along the trajectory will give you the overall work done on the rubber band. This can be calculated by summing all the individual work values. This is known as the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy.

2- Your equations for both scenarios are correct. In the first scenario, when you are holding the bag still, the work done is equal to the product of the mass of the groceries, gravitational acceleration, and the height of the bag from the ground. This is because the bag is not moving, so there is no change in its kinetic energy. In the second scenario, when you are walking across the parking lot with the bag, the work done is equal to the product of the mass of the groceries, gravitational acceleration, and the distance you walk. This is because as you move, the bag is also moving and therefore has a change in its kinetic energy.