A beam resting on two pivots has a length of L = 9.00 m and mass M =81.0 kg. The pivot under the left end exerts a normal force n1 on the beam, and the second pivot placed a distance 4.00 m from the left end exerts a normal force n2. A woman of mass m= 43.0 kg steps onto the left end of the beam and begins walking to the right as in the figure. The goal is to find the woman’s position when the beam begins to tip. (c) Use the force equation of equilibrium to find the value of n2 when the beam is about to tip.

To find the value of n2 when the beam is about to tip, we need to use the force equation of equilibrium.

The force equation of equilibrium states that the sum of all the forces acting on an object must be equal to zero for it to be in equilibrium.

In this case, when the beam is about to tip, the net torque acting on it must be zero. Torque is the product of the force and the distance from the pivot point.

Let's start by considering the forces and torques acting on the beam and the woman. There are four forces acting on the beam:

1. The weight of the beam acting at its center of mass.
2. The normal force n1 from the pivot under the left end of the beam.
3. The weight of the woman acting at the left end of the beam.
4. The normal force n2 from the pivot placed 4.00 m from the left end of the beam.

The weight of the beam can be calculated using the formula: weight = mass * acceleration due to gravity. In this case, the beam's weight is W_beam = M * g.

The weight of the woman is W_woman = m * g.

Now, let's calculate the torques acting on the beam. The torque due to the weight of the beam can be calculated as: Torque_beam = W_beam * (L/2), since the weight acts at the center of mass.

The torque due to the woman's weight can be calculated as: Torque_woman = W_woman * L.

Since the beam is about to tip, the net torque must be zero. Therefore, the sum of the torques acting on the beam must be equal to zero: Torque_beam + Torque_woman - n1 * 0 - n2 * (L-4) = 0.

Substituting the calculated values and rearranging the equation, we can solve for n2:

M * g * (L/2) + m * g * L - n2 * (L-4) = 0.

Now we can solve this equation to find the value of n2.