(II) A 2500-kg trailer is attached to a stationary truck at...

(II) A 2500-kg trailer is attached to a stationary truck at point B, Fig. 9-61. Determine the normal force exerted by the road on the rear tires at A, and the vertical force exerted on the trailer by the support B.
FIGURE 9–61 Problem 21. (Figure can't copy)

Key Concepts

Center of Gravity

The center of gravity is the point in an object where the entire weight of the body can be considered to act. In static analyses, assuming that the weight acts at the center of gravity simplifies the calculation of moments and reaction forces in equilibrium problems.

Reaction Forces

Reaction forces are the forces exerted by supports or connections in response to applied loads. They are determined by applying static equilibrium equations, both for forces and moments, and are crucial for understanding how structures support and distribute loads.

Moments and Torque

Moments (or torque) measure the tendency of a force to cause rotation about a pivot or axis. In static problems, calculating the moments about a chosen point allows one to determine unknown reaction forces by ensuring that the net moment is zero.

Static Equilibrium

Static equilibrium refers to the condition in which an object is at rest and the net force and net moment acting on it are zero. This concept is crucial for analyzing structures and bodies that do not accelerate, ensuring that forces and moments balance perfectly in both the horizontal and vertical directions.

Free-Body Diagram

A free-body diagram is a graphical representation that isolates a body and shows all the external forces and moments acting on it. This tool is essential for visualizing how different forces interact, which simplifies the process of applying the static equilibrium conditions to solve for unknown forces.

Transcript

00:01 All right, chapter 9, problem 21.

00:04 We have a 2 ,500 kilogram trailer is attached to a stationary truck at point b in figure 9 -61.

00:13 Determine the normal force inserted by the road on the rear tires at a, and the vertical force inserted on the trailer but support b.

00:21 Let's go back to our question.

00:23 Okay, so i've drawn the free body diagram here, and let's just go through a couple things real quick, just to start off with.

00:32 So the rear the rear tires are going to feel a force from the ground and that's what faa is going to be there the trailer itself has the weight like starting from this m equals 2 ,500 kilograms and then with gravity you know you're going to have a weight on the trailer so that's what's in the middle and then there's also a force on the trailer caused by the support in the truck that's fb so what we're going to want to do here is use newton's second law to our advantage.

01:07 It's important that the system is in equilibrium because this makes sure the second two points are true.

01:15 Some of the torques and the sum of the forces are both zero.

01:19 And we also want to note that 2 .5 meters is the distance between the rear tires and the center of mass of the trailer and the center of mass of the trailer.

01:33 The distance between the center of mass of the trailer and the support is 5 .5 meters.

01:39 So what do we want to do first? we can use either the sum of the torques equal zero or the sum of the forces equal zero.

01:45 I just decided to use some of the torques.

01:47 And i chose my pivot to be around d...

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