In the figure below, a uniform beam of weight 420 N and length 3.2 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N.

Question

In the figure below, a uniform beam of weight 420 N and length 3.2 m is suspended horizontally. On the left it is hinged to a wall; on the right is it supported by a cable bolted to the wall at distance D above the beam. The least tension that will snap the cable is 1200 N.

(a) What value of D corresponds to that tension?
m

(b) Give any value for D that won't snap the cable.
m

Answer 1

Casey, Mark, Phillipe -- and other names you've just posted -- it's not necessary to change names for each post. You'll get more help if you use the same name AND tell us what you know about solving the problem.

Answer 2

To answer both parts (a) and (b) of the question, we need to understand the equilibrium requirement for the beam. In order for the beam to remain in static equilibrium, the sum of the clockwise torques must be equal to the sum of the counterclockwise torques.

Let's consider the forces acting on the beam:

1. Weight of the beam (420 N): This force acts vertically downward from the center of the beam.

2. Tension in the cable: This force acts vertically upward, perpendicular to the beam, at a distance D above the beam.

3. Reaction force at the hinge: This force acts vertically upward at the left end of the beam, preventing it from rotating.

To find the value of D that corresponds to the tension of 1200 N, we can set up an equation using torques:

Sum of clockwise torques = Sum of counterclockwise torques

Clockwise torque due to the weight of the beam = (420 N) * (3.2 m/2)

Counterclockwise torque due to the tension in the cable = (1200 N) * D

Since the beam is in static equilibrium, these torques must be equal:

(420 N) * (3.2 m/2) = (1200 N) * D

Simplifying the equation gives us:

672 N·m = 1200 N·D

To find the value of D, we can rearrange the equation:

D = (672 N·m) / (1200 N)

D ≈ 0.56 m

Therefore, the value of D that corresponds to the tension of 1200 N is approximately 0.56 m.

For part (b), any value of D that is less than or equal to 0.56 m won't snap the cable. So, you can choose any value of D less than or equal to 0.56 m as an answer for part (b).