A hungry bear weighing 700 N walks out on a beam in an attempt to retrieve a basket of goodies h

step 1 In this problem, we have a bear that is standing on a platform here, and the bear is inching his

A hungry bear weighing 700 N walks out on a beam in an...

A hungry bear weighing 700 $\mathrm{N}$ walks out on a beam in an attempt to retrieve a basket of goodies hanging at the end of the beam (Fig. Pl2.43). The beam is uniform, weighs $200 \mathrm{N},$ and is 6.00 $\mathrm{m}$ long, and it is supported by a wire at an angle of $\theta=60.0^{\circ} .$ The basket weighs 80.0 $\mathrm{N}$ . (a) Draw a force diagram for the beam. (b) When the bear is at $x=$ $1.00 \mathrm{m},$ find the tension in the wire supporting the beam and the components of the force exerted by the wall on the left end of the beam. (c) What If? If the wire can withstand a maximum tension of 900 $\mathrm{N}$ , what is the maximum distance the bear can walk before the wire breaks?

Key Concepts

Resolving Force Components

Force resolution is the process of breaking a force into its horizontal and vertical components, especially when the force is applied at an angle. This technique is vital when analyzing the tension in the supporting cable, as it requires evaluating how its angled components contribute to balancing the vertical loads and providing horizontal support through the reaction at the wall. Understanding vector components simplifies the application of the equilibrium conditions in two dimensions.

Torque and Moment Calculation

Torque, or moment, is the tendency of a force to cause rotation about a pivot or axis. It is calculated by multiplying the force by the perpendicular distance (moment arm) to the pivot point. In problems involving beams and levers, such as this one, setting the sum of torques around a chosen pivot equal to zero is a fundamental step in determining unknown forces like the tension in the wire or the allowable distance the bear can move without breaking the system.

Free-Body Diagram

A free?body diagram is a simplified representation that shows all the external forces acting on an object, such as weights, applied forces, and reaction forces. In this context, it involves illustrating the force due to the beams’ self?weight, the bear, the basket, the tension in the supporting cable, and the reaction forces from the wall. This diagram is essential to set up the problem correctly before applying further analysis using equilibrium conditions.

Static Equilibrium

Static equilibrium refers to the state where an object or a system is at rest, and both the net force and net moment (torque) acting on it are zero. This principle is crucial in analyzing the beam because it allows the setup of equations where the sum of forces in both the horizontal and vertical directions, as well as the sum of moments about any pivot, must cancel out. This ensures that the beam does not translate or rotate under the applied loads.

Transcript

Please give Ace some feedback