A horizontal beam of length 4 m and mass 7.0 kg has a mass of 2.0 kg and width 0.8 m sitting at the end of the beam (see the following figure). What is the torque due to gravity (in N · m) on the beam–block system about the support at the wall? (Enter the magnitude.)

To find the torque due to gravity on the beam-block system, we first need to determine the force of gravity acting on the block, using the formula:

Force of gravity = mass * acceleration due to gravity

Since the mass of the block is given as 2.0 kg and the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate:

Force of gravity = 2.0 kg * 9.8 m/s^2 = 19.6 N

Next, we need to find the distance between the support at the wall and the line of action of the force of gravity. This distance is the horizontal distance from the support to the point where the force of gravity is acting, which is the length of the beam.

The torque (τ) is then given by the formula:

τ = force * distance

Since we have the force of gravity as 19.6 N and the distance is given as 4.0 m, we can calculate:

τ = 19.6 N * 4.0 m = 78.4 N·m

Therefore, the torque due to gravity on the beam-block system about the support at the wall is 78.4 N·m.