Question

A block is held at rest against a wall by a force of magnitude F exerted at an angle theta from the horizontal, as shown in the figure above. Let Fg be the gravitational force exerted by Earth on the block, Fn be the normal force exerted by the wall on the block, an Ff be the frictional force exerted by the wall on the brick. Which of the following statements about the magnitude of the forces on the block must be true? Select two answers.
A.) F = Fg / Sin(theta)
B.) Fcos(theta) = Fn
C.) Fsin(theta) = Fg + or - Ff
D.) F = Fg + Fn + or - Ff

Answer 1

Answers:

B.) $F cos\theta=F_{n}$

C.) $F sin\theta=F_{g} \pm F_{f}$

Explanation:

The image attached shows the way the force $F$ is acting on the block. Now, if we draw a free body diagram of the situation and write the equations for the Net Force in X and Y, we will have the following:

Net Force in X:

$-F_{n}+F cos\theta=0$ (1)

Where:

$F_{n}$ is the Normal force

$F$ is the magnitude of the force exerted on the block

$\theta$ is the angle

Net Force in Y:

$F sin\theta \pm F_{f}-F_{g}=0$ (2)

Where:

$F_{f}$ is the Friction force (it is expresed with the $\pm$ sign because this force may be up or down, we cannot know because the block is at rest)

$F_{g}$ is the gravity force

Rewrittin (1):

$F cos\theta=F_{n}$ (3) This is according to option B

Rewritting (2):

$F sin\theta=F_{g}\pm F_{f}$ (3) This is according to option C