M-3  Static Forces and Moments

OBJECTIVE: To check experimentally the conditions for equilibrium of a rigid body.

APPARATUS:

Model of rigid derrick, slotted masses and weight hangers, knife edge (mounted in wall bracket), vernier caliper, single pan balance.

INTRODUCTION:

Equilibrium requires that the net linear acceleration and the net angular acceleration be zero. Hence $\sum \vec{F}_{\mbox{\small ext}} = 0$ and $\sum \vec{\tau}_{\mbox{\small ext}} = 0$. We treat the rigid derrick as a two dimensional structure so the vector equations become: $\sum \vec{F}_{x} = 0$, $\sum \vec{F}_y = 0$ and $\sum \vec{\tau}= 0$. The choice of the perpendicular axis about which one computes torques is arbitrary so in part 4 below we choose an axis which simplifies calculations.

Pre-lab Quiz

• Expt. M03 Quiz

SUGGESTED PROCEDURES:

1. Place a load of about 2 kg for $m_2$.
2. Determine experimentally the force $m_3$ to hold the derrick in equilibrium with the top member level. Since this is an unstable equilibrium, adjust $m_3$ so that the derrick will fall either way when displaced equally from equilibrium. To find the uncertainty in $m_3$ increase or decrease $m_3$ until you know the smallest force $m_3$ which is definitely too large and the largest which is definitely too small.

3.

Weigh the derrick (use single pan balance) and find the horizontal distance between the center of the stirrup and the vertical line through the center of gravity (c.g.) of the derrick. (Use the knife edge mounted in a wall bracket for locating the c.g.)

4.

Calculate how accurately the $\sum \vec{\tau}_{\mbox{\small ext}} = 0$ condition is satisfied about the point where the lower stirrup supports the derrick. Note: distance from rotation axis must include stirrup axle radius (use vernier caliper).

5.

Calculate the force $\vec{F}$ exerted by the stirrup on the derrick.

6.

Choose an axis that is not on the line of action of any force and calculate how closely is satisfied about that axis. Is the discrepancy reasonable? Make your answer as quantitative as you can. (Include the uncertainty in $\vec{F}$ and any other measurements).