Why don't we just go straight?

Classical Mechanics Level 3

A 1 kg 1\text{ kg} object is lifted from point A to point B through two different pathways as shown in the figure above. What are the respective amounts of work done in the left and right figures?

The gravitational acceleration is g = 9.8 m/s 2 . g=9.8\text{ m/s}^2.

294 J, 196 J 196 J, 196 J 196 J, 294 J 0 J, 0 J

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Ankit Vijay by Ankit Vijay , 22, India

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6 solutions

Discussions for this problem are now closed

Ankit Vijay
Jun 12, 2014

Work done is change in gravitational potential energy and G.P.E. is independent of path W = m g h = 1 × 9.8 × 20 = 196 J W = mgh = 1 × 9.8 × 20 = 196 J in both cases

11 Helpful 0 Interesting 0 Brilliant 0 Confused

how the distance at figure 2 equal 20

Mahmoud Ibrahim - 6 years, 11 months ago

See only verticle distance. Dont count horizontal distance..

Inzamam Ashraf - 6 years, 11 months ago

Victor you are partially correct.. The questions needs to specify - "work done by whom?"

Gravity and h, both are vectors. so the direction of gravity .. as you assume will be negative (vert. downwards). This results in negative "work done" which is because while gravity acts vertically downwards and the displacement was vertically upward. -> Work done by gravity is -196J. (negative)

On the other hand, there was some force (F) that displaced the body by 2m vertically up. If this force was vertically upward (ie same as the direction of the displacement) .. this results in "positive" work -> Work done by force = 196J (positive)

Allen George - 6 years, 12 months ago

Should the gravity not be negative?

Victor Song - 7 years ago

No...anyway why would gravity be negative that means it will repel everything from it?

Ankit Vijay - 7 years ago

"Negative" means that the object is moving against the gravity ,anyway height will be negative too because the same reason, so they will fade each other

Sarah Yahia - 6 years, 12 months ago
Rajaa Sahil
Jun 23, 2014

Work done is independent of path followed, so in both case the formula is used W=mgh.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Bernardo Sulzbach
Jun 17, 2014

It is not zero. It is the same in both cases. There is only one alternative left. Go for it.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

This solution has been marked wrong. Why is it "It is not zero. It is the same in both cases."?

Jalees Mughal
Jul 25, 2014

Work done in conservative field is independent of Path...

1 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

You should show that the work done calculated to be 196 J 196 J .

Independently of the "moves" of the block, the important its the High (h), so => W = m.g.h => 1.9,8.20 = 196J

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Paola Ramírez
Jan 4, 2015

W = m g h = 9.8 × 1 × 20 = 196 J W= mgh=9.8 \times 1 \times 20=196 J , h h is equal in both cases thus W W is equal 196 J , 196 J \boxed{196 J,196 J}

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Moderator note:

For clarification, you should mention that the work done is independent of its path.

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