• Support PF! Buy your school textbooks, materials and every day products Here!

Comparing work done(Please help me mark my concept)

  • Thread starter Yh Hoo
  • Start date
  • #1
73
0
For both situation, the person oh the ship is pulling the rope with a particular constant magnitude of force, F for a fixed duration, t. Because the medium of force F is a light inextensible rope, so force doing work is in the form of tension. Treat both the person and the boat as an entity and having a combined mass of m. Also the tension in the rope due to that person's pulling force is assumed to maintain for always.

Now for situation A, the object pulls the rope anchor on a fixed pole. The tension in the rope should then be equal to F. By newton's third law, the rope reaction force pulls back the object.

Situation A
# Acceleration of objects under action of force, a = F/m

# Displacement of objects for duration t, s = (1/2) (a) (t^2)
= (1/2) (F/m) (t^2)

# Work done by F, W_A= F s
= F (1/2) (F/m) (t^2)
= (1/2) (F^2/m) (t^2)

For situation B, assume both objects freely floating on the sea having equal mass, m.

Situation B
# Acceleration of objects under action of force, a = F/2m

# Displacement of object 1 for duration t, s = (1/2) (a) (t^2)
= (1/2) (F/2m) (t^2)

Total displacement occurs = 2 s
=2 ( 1/2) ( F/2m) (t^2)
= (F/2m) (t^2)

# Work done by F, W_A= F s
= F ( 1/2) ( F/m) (t^2)
= (1/2) (F^2/m) (t^2) (Same as that in situation A)


Is my calculation true?? Thanks for your verifying.
 

Attachments

Last edited:

Answers and Replies

  • #2
Philip Wood
Gold Member
1,221
75
Yes, I think so. Each boat in (b) acquires the same KE as the single boat in (a). So twice as much work is done overall in case (b) as in (a).
 
  • #3
73
0
Thanks a lot. U help me a lot.
 

Related Threads for: Comparing work done(Please help me mark my concept)

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
1K
  • Last Post
Replies
10
Views
2K
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
Replies
4
Views
9K
Replies
9
Views
2K
Top