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The answer is C.

I'm thoroughly confused! The question is asking for when the magnitude of the vertical component of the force that the wall exerts on the left end of the beam is the smallest. How can a wall that is perpendicular to the beam exert a force in any direction other than directly to the right? When would there ever be a vertical component?

Am I missing some sort of fundamental understanding about how forces work? If I exert a force on a wall by pushing it with my hand and forearm at an angle, by Newton's third law, is the wall capable of exerting a force on my arm at the same angle? Or is it only going to exert a force equal to the horizontal component of my force?

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    $\begingroup$ Static friction or a pinned joint at the wall. Without that, the beam will have a net torque around the outer end due to the weight acting through the center of mass. $\endgroup$
    – Bill N
    Commented May 2, 2017 at 2:48
  • $\begingroup$ AP Physics 1? . $\endgroup$
    – lithium123
    Commented May 2, 2017 at 2:53
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    $\begingroup$ It is not uncommon to do similar problems where the wall-beam interaction is restricted to being normal when first encountering statics, but that is a special case. In general you expect both normal and parallel forces. If the parallel force is purely frictive then it has the usual relationship with the normal force, of course. $\endgroup$
    – dmckee --- ex-moderator kitten
    Commented May 2, 2017 at 3:07
  • $\begingroup$ The beam and support cable are attached to the wall (i.e. not sliding). The joint at which they are attached can exert both parallel and normal forces (otherwise, the beam and support cable wouldn't be "attached," they would slide down the wall). $\endgroup$
    – probably_someone
    Commented Jul 10, 2018 at 17:26

3 Answers 3

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Consider the forces on the beam:

Tension in the cable pulls up and left on the right end of the beam, which would tend to torque it counterclockwise and translate it to the left.

Gravity pulls down on the center of the beam (effectively) which would tend to translate it downward.

If the beam is not rotating or translating, there must be some rightward force to counter translation due to the cable and some upward force on the left end to counter the torque (and together with the cable, prevent falling).

The final set of forces on the beam are downward gravity, up-right compression from the wall and up-left tension from the cable, which all balance out to keep the beam in place and level.

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If a roller bearing was to be put on the left side of the beam it would fall straight down without help from the upward acting frictional force at the wall.

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Am I missing some sort of fundamental understanding about how forces work?

No. You are just forgetting about friction.

If I exert a force on a wall by pushing it with my hand and forearm at an angle, by Newton's third law, is the wall capable of exerting a force on my arm at the same angle?

Sure. The wall produces a normal force to balance the perpendicular part of the push and a friction force to balance the parallel part of the push. The "wall force" at an angle is just their combination, the resulting force.

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