A tow truck pulls a car that is stuck in the mud, with a force of 2500 N as in Fig. P5.27. The t

A tow truck pulls a car that is stuck in the mud, with a...

A tow truck pulls a car that is stuck in the mud, with a force of $2500 \mathrm{N}$ as in Fig. P5.27. The tow cable is under tension and therefore pulls downward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars $\mathrm{A}$ and $\mathrm{B}$. Each bar is a strut: that is, each is a bar whose weight is small compared to the forces it exerts, and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed parallel to its length. Determine the force of tension or compression in each strut. Proceed as follows: Make a guess as to which way (pushing or pulling) each force acts on the top pin. Draw a free-body diagram of the pin. Use the condition for equilibrium of the pin to translate the free-body diagram into equations. From the equations calculate the forces exerted by struts $A$ and $B$ If you obtain a positive answer, you correctly guessed the direction of the force. A negative answer means the direction should be reversed, but the absolute value correctly gives the magnitude of the force. If a strut pulls on a pin, it is in tension. If it pushes, the strut is in compression. Identify whether each strut is in tension or in compression. (FIGURE CAN'T COPY)

A tow truck pulls a car that is stuck in the mud, with a force of $2500 \mathrm{N}$ as in Fig. P5.27. The tow cable is under tension and therefore pulls downward and to the left on the pin at its upper end. The light pin is held in equilibrium by forces exerted by the two bars $\mathrm{A}$ and $\mathrm{B}$. Each bar is a strut: that is, each is a bar whose weight is small compared to the forces it exerts, and which exerts forces only through hinge pins at its ends. Each strut exerts a force directed parallel to its length. Determine the force of tension or compression in each strut. Proceed as follows:
Make a guess as to which way (pushing or pulling) each force acts on the top pin. Draw a free-body diagram of the pin. Use the condition for equilibrium of the pin to translate the free-body diagram into equations. From the equations calculate the forces exerted by struts $A$ and $B$ If you obtain a positive answer, you correctly guessed the direction of the force. A negative answer means the direction should be reversed, but the absolute value correctly gives the magnitude of the force. If a strut pulls on a pin, it is in tension. If it pushes, the strut is in compression. Identify whether each strut is in tension or in compression.
(FIGURE CAN'T COPY)

Key Concepts

Static Equilibrium

This concept refers to a state where a system or object is at rest because the sum of all forces and moments acting on it is zero. In structural mechanics, ensuring static equilibrium is fundamental for analyzing forces in components, as it allows the derivation of relationships (equations) that the forces must satisfy for the system to remain stable.

Free-Body Diagram

A free-body diagram is a simplified representation of an object where all the external forces (and moments) acting on it are isolated and sketched. This tool is essential in statics, as it helps in visualizing and setting up the balance of forces and moments that define the system's equilibrium.

Force Resolution

Force resolution involves breaking down a force into its horizontal and vertical components (or components in any chosen set of axes). This process is key in statics because it enables the application of equilibrium equations separately along each axis, simplifying the analysis of complex force systems.

Tension and Compression in Structural Members

Understanding tension and compression is crucial when analyzing members such as struts. Tension refers to forces that pull or elongate a component, while compression refers to forces that push or shorten it. Correctly identifying whether a member is in tension or compression helps predict its behavior under load and is necessary for designing safe and efficient structures.

Pin or Hinge Connections

Pin or hinge connections allow rotation but restrict translations in at least two directions. They are critical in structural analyses because they define how forces are transmitted between connected members. Analyzing forces at these joints, often using free-body diagrams, facilitates the determination of internal forces in structures.

Transcript

00:03 All right, so in this problem, we're focused on the pin, on the tow truck, where the struts connect and where the cable connects.

00:25 So i'll draw a diagram here, and you can draw your own diagram.

00:34 It might look a little different because you might have different predictions for where the forces are going.

00:43 A downward and to the left force from the tow cable.

00:47 I think we can agree on that.

00:49 I'm going to label this f .c.

00:54 C for cable.

00:56 And then the other strut, i think it's pulling down and to the right.

01:09 I'll label this.

01:12 What strut is this? let's see.

01:15 This strut b.

01:17 So i'll label this fb.

01:25 The reason why i think it's going this, it's pulling this way is because the net force on this pin is zero, because otherwise it would be moving.

01:46 So in order for the horizontal components to cancel out, that means that f .c.

01:59 I hat must be equal.

02:02 To the opposite of fb i had.

02:08 We don't have to worry about a horizontal component for strut a, because strut a is perfectly up and down.

02:16 So it has no horizontal component.

02:21 So lastly, my prediction is that strut a will be upward.

02:37 And like before, i think this is because both of these have a downward direction.

02:49 So in order to cancel those out, f .a.

03:03 Must equal due to third law, f .j.

03:17 J hat plus fb .j.

03:33 And we have this side be negative because, well, they gave us that f .c.

03:46 Equals 2 ,500 dutons.