Question

A man plans to use a 2 metre crowbar to lift a rock by putting a pivot 0,8 m from

the rock. One end of the crowbar will be under the rock and he will push down
on the other end with a force of 400 N. The mass of the rock is 50 kg.
1.Will the man be able to move the rock? Show how you worked out your
answer.
2.The man’s daughter says that she can move the rock although her force
on the other end is only 200 N. Explain how this is possible

Answer 1

The answer is 0.58 meters. I agree with the working shown below. I did the same on paper, and it is the right answer. 

Answer 2

1. The man will be able to move the rock. See diagram.
Moment of Man's force : 400 N * 1.2 meter = 480 N-m
Rock's Weight = 50 Kg * 9.8 m/sec² = 490 Newtons
Moment of Rock's weight : 490 N * 0.80 meters = 392 N-m

Moment of Man's Force is MORE : 480 N-m > 392 N-m
So man will be able to lift the rock.

2. Let is look at the diagram - second one.
Let us assume that the fulcrum (Pivot) is placed at X meters from the rock.
So moment of Girl's force about Pivot = 200 N * (2 - X) meters = 400 - 200 X
Moment of Rock's weight = 490 N * X = 490 X

As the Girl is able to lift the rock, 400 - 200 X > 490 X
Hence 400 > 200 X + 490 X
400 > 690 X
X < 400/690 = 0.58 meters
If the Pivot is placed closer than 0.58 meters or 58 cm to the Rock, then
she can lift the rock.