Question

A uniform plank 8.00 m in length with mass 30.0 kg is supported at two points located 1.00 m and 5.00 m, respectively, from the left-hand end. What is the maximum additional mass you could place on the right-hand end of the plank and have the plank still be at rest

Answer 1

To determine the maximum additional mass that can be placed on the right-hand end of the plank while keeping it at rest, we need to consider the principle of static equilibrium and calculate the torques exerted by the additional mass, the plank, and the mass already on it. The torque exerted by the additional mass should be balanced by the torques exerted by the weights of the plank and the mass already on it.

Step-by-step explanation:

To determine the maximum additional mass that can be placed on the right-hand end of the plank while keeping it at rest, we need to consider the principle of static equilibrium. Static equilibrium occurs when the sum of the forces acting on an object is zero and the sum of the torques is zero.

In this case, the plank is supported at two points, 1.00 m and 5.00 m from the left-hand end. The torque exerted by the additional mass on the right-hand end of the plank should be balanced by the torques exerted by the weights of the plank and the mass already on it.

Let's assume that the maximum additional mass that can be placed on the right-hand end is M. The torque exerted by this mass will be M multiplied by the distance from the right-hand end of the plank to the center of mass of the additional mass. In order to keep the plank at rest, this torque should be equal to the sum of the torques exerted by the weights of the plank and the mass already on it. Using this information, we can calculate the maximum additional mass that can be placed on the right-hand end of the plank.