Calculating Leverage and Mechanical Advantage

[Ignoramus]

1. A pair of brothers have a 20kg, 3.5m plank they want to use as a lever. They use a fulcrum which is 0.75m from the load mass. If they push down one end of the lever with a force of 210N, then they can move the Load mass away. What is the upward force exerted on the large mass? If the mechanical advantage is defined as a ratio of resistance force compared to the effort force, how much mechanical advantage is gained by the lever?

Homework Equations

F_ed_e= F_Ld_L


3. I used the 210N as the F_e, and 2.75 as the d_e set equal to F_L multiplied by 0.75 for d_L Then I solve for the F_L. I'm not sure if the answer I get is the upward force, though I would assume it is...As for the second question, I have no idea where to begin on that. Thanks!

 

[LowlyPion]

It may be a little more complicated.

The plank has mass. And assuming it has uniform density over its length then you have an unbalanced weight just from the plank alone don't you?

 

[PhanthomJay]

you forgot to consider the torque due to the weight of the 20 kg lever itself. What does the sum of torque equation tell you about the direction of the force at the end you label as "L"? Mechanical advantage is just F_L / F_e.

 

[Ignoramus]

Our teacher is notorious for giving us variables that are not needed, so I'm doubting the mass of the plank matters. Plus the fact that we've never had to mess with the mass of the lever itself. Although, the mass is 210 N, so dividing by 9.8,you find the mass of the load is greater than the plank.

I have no idea what the sum of torque equation is, since we just started on simple machines :\

 

[LowlyPion]

Unfortunately it does matter, the reputation of your teacher not withstanding.

The effect is sizable. Because basically you have the distance of the center of mass acting at a distance from the fulcrum. That looks like 20*9.8 N acting at about a meter from the fulcrum.

 

[Ignoramus]

So...what should I do?


Help :(

 

[LowlyPion]

Draw a diagram.

Add up your torques.

The total net torque/distance to the mass is the force delivered to the mass.