Question

Assume you have a 2.5 meter long piece of lumber (your "lever"), which has a mass of about 5.9 kg, with a CG in the middle. Also you will always exert a force of 400N in the following problems.  

1. What is the maximum weight you could lift (the "load") with a Class 1 lever if you exerted your force at the end of the lever, the fulcrum is in the middle of the lever, and load at the other end of the lever?

2. What is the maximum load you could lift with the above lever if you moved the fulcrum to 0.5 meters from the load end of the lever? (Remember: the lever has its own mass.)

3. What is the maximum load you could lift with a class 2 lever if the load is in the middle of the lever and the fulcrum is at one end and you are lifting at the other end?

4. What is the maximum load you could lift with a Class 2 lever if the load 0.5 meters from the fulcrum?

5. What is the maximum load you could lift with a Class 3 lever if the load is at one end, the fulcrum is at the other end, and you lift in the middle?

6. What is the maximum load you could lift with a Class 3 lever if you lift 0.5 meters from the load end of the lever?

Answer 1

Length of lever , mass of lever , Force applied (effort)

Load is

1)

Class 1 lever:

From the fulcrum the distance of is , distance of is and distance of is

Net Torque on the lever about fulcrum is zero,

Mass equivalent to is

Hence the maximum weight that can be lifted is or

2)

Now the fulcrum is shifted to 0.5 m from the load end.

Now forces acting on lever are, at one end, at the middle ( at distance ) and   at the other end (at distance  )

From the fulcrum the distance of is to the left of fulcrum , distance of is to the left of fulcrum and distance of is to the right of fulcrum

Net Torque on the lever about fulcrum is zero,

Mass equivalent to is

Hence the maximum weight that can be lifted is or

3)

Class 2 lever:

Now the load is at distance   to the left  from the fulcrum , weight of lever is at distance to the left from the fulcrum, effort is at a distance to the left of fulcrum.

Net Torque on the lever about fulcrum is zero,

and its mass equivalent is

Hence the maximum weight that can be lifted is or

4)

If the load at a distance of 0.5 m from the fulcrum,

Now the load is at distance   to the left  from the fulcrum , weight of lever is at distance to the left from the fulcrum, effort is at a distance to the left of fulcrum.

Net Torque on the lever about fulcrum is zero,

and its mass equivalent is

Hence the maximum weight that can be lifted is or

5)

Class 3 lever:

Now the load is at distance   to the right from the fulcrum , weight of lever is at distance to the right from the fulcrum, effort is at a distance to the right of fulcrum.

Net Torque on the lever about fulcrum is zero,

and its mass equivalent is

Hence the maximum weight that can be lifted is or

6)

Now the effort F is at 0.5 m to the left from the load end.

Now the load is at distance   to the right from the fulcrum , weight of lever is at distance to the right from the fulcrum, effort is at a distance to the right of fulcrum.

Net Torque on the lever about fulcrum is zero,

,